Skip to main content
SpringerLink
Log in
Book cover

Perplexing Problems in Probability pp 1–33Cite as

Harry Kesten’s Publications

A Personal Perspective

  • Chapter

Part of the book series: Progress in Probability ((PRPR,volume 44))

Abstract

Writing about Harry Kesten’s life work is a daunting task. At of the writing of this paper, he has published almost 150 papers totaling more than 5000 pages. The topics range from refined results for the classical topics of random walks, renewal theory, Lévy processes, and branching processes to questions of interest in statistical mechanics: first passage percolation, percolation, DLA, and the models named after Ising, Potts, and Heisenberg. In most cases Harry has solved other people’s problems, so his publication list makes excursions into dozens of other topics from the local times for Markov processes [25, 43] to existence and uniqueness of Markov random fields [54]; from the speed of convergence of martingales [59] and properties of positive harmonic functions [61] to Chung-type laws of the iterated logarithm [143].

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aizenman, M. and Barsky, D.J. (1987) Sharpness of the phase transition in percolation models. Comm. Math. Phys. 86, 1–48

    Article  MathSciNet  Google Scholar 

  2. Aizenman, M., Chayes, J.T., Chayes, L., Föhlich, J., and Russo, L. (1983) On a sharp transition from area law to perimeter law in a system of random surfaces. Comm. Math. Phys. 92, 19–69

    Article  MathSciNet  MATH  Google Scholar 

  3. Aizenman, M., Chayes, J.T., Chayes, L., and Newman, C.M. (1988) Discontinuity of the magnetization in the one dimensional 1/|x−y|2 Ising and Potts models. J. Stat. Phys. 50, 1–40

    Article  MathSciNet  MATH  Google Scholar 

  4. Aizenman, M., and Lebowitz, J. (1988) Metastability effects in bootstrap percolation. J. Stat. Phys. 21, 3801–3813

    MathSciNet  MATH  Google Scholar 

  5. Aizenman, M. and Newman, C.M. (1984) Tree graph inequalities and critical behavior in percolation models. J. Stat. Phys. 36, 107–143

    Article  MathSciNet  MATH  Google Scholar 

  6. Aizenman, M. and Newman, C.M. (1986) Discontinuity of the percolation density in one dimensional 1/1x–y1 2percolation models. Comm. Math. Phys. 107, 611–647

    Article  MathSciNet  MATH  Google Scholar 

  7. Aldous, D. (1993) The continuum random tree III. Ann. Pmb. 21, 248–289

    MathSciNet  MATH  Google Scholar 

  8. Aldous, D. and Steele, J.M. (1992) Asymptotics for Euclidean minimal spanning trees on random points. Prob. Th. Rel. Fields. 92, 247–258

    Article  MathSciNet  MATH  Google Scholar 

  9. Alexander, K.S. (1993) A note on some rates of convergence for first passage percolation Ann. Appl. Prob. 3, 81–90

    Article  MATH  Google Scholar 

  10. Alexander, K.S. (1996) The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees. Ann. Appl. Prob. 3, 1033–1046

    Google Scholar 

  11. Barsky, D.J. and Aizenman, M. (1988) Percolation critical exponents under the triangle condition. Preprint.

    Google Scholar 

  12. Bezuidenhout, C. and Grimmett, G. (1990) The critical contact process dies out. Ann. Prob. 18, 1462–1482

    Article  MathSciNet  MATH  Google Scholar 

  13. Bezuidenhout, C. and Grimmett, G. (1991) Exponential decay for subcritical contact and percolation processes. Ann. Prob. 19, 984–1009

    Article  MathSciNet  MATH  Google Scholar 

  14. Bramson, M., Durrett, R., and Swindle, G. (1989) Statistical mechanics of crabgrass. Ann. Prob. 17, 444–481

    Article  MathSciNet  MATH  Google Scholar 

  15. Bramson, M. and Griffeath, D. (1980) Asymptotics for interacting particle systems on Zd. Z. fur Wahr. 53, 183–196

    Article  MathSciNet  MATH  Google Scholar 

  16. Bricmont, J. and Kupiainen, A. (199la) Renormalization-group for diffusion in a random medium. Phys. Rev. Letters 66, 1689–1692

    Article  MathSciNet  MATH  Google Scholar 

  17. Bricmont, J. and Kupiainen, A. (1991b) Random walks in asymmetric environments. Comm. Math. Phys. 142, 345–420

    Article  MathSciNet  MATH  Google Scholar 

  18. Broadbent, S.R. and Hammersley, J.M. (1957) Percolation processes. Proc. Camb. Phil. Soc. 53, 629–645

    Article  MathSciNet  MATH  Google Scholar 

  19. Burton, R.M., and Keane, M. (1988) Density and uniqueness in percolation. Comm. Math. Phys. 121, 501–505

    Article  MathSciNet  Google Scholar 

  20. Cohen, J.E., Kesten, H., and Newman, C.M. (1984) Random Matrices and Their Applications. Contemporary Mathematics, Vol. 50, American Mathematical Society, Providence, RI

    Google Scholar 

  21. Cohen, J.E., and Newman, C.M. (1984) The stability of large random matrices and their products. Ann. Prob. 12, 283–310

    Article  MathSciNet  MATH  Google Scholar 

  22. Cox, J.T. and Durrett, R. (1981) Some limit theorems for percolation processes with necessary and sufficient conditions. Ann. Prob. 9, 583–603

    Article  MathSciNet  MATH  Google Scholar 

  23. Doeblin, W. (1940) Remarques sur la theorie métrique des fractions continues. Compositio Math. 7, 353–371

    MathSciNet  MATH  Google Scholar 

  24. Durrett, R. (1984) Oriented percolation in two dimensions. Ann. Prob. 12, 999–1040

    Article  MathSciNet  MATH  Google Scholar 

  25. Durrett, R. (1995a) Ten lectures on particle systems. Pages 97–201 in Lecture Notes in Mathematics 1608, Springer-Verlag, New York

    Google Scholar 

  26. Durrett, R. (1995b) Probability: Theory and Examples. 2nd Edition. Duxbury Press, Belmont, CA

    Google Scholar 

  27. Durrett, R. and Liggett, T.M. (1981) The shape of the limit set in Richardson’s growth model. Ann. Prob. 9, 186–193

    Article  MathSciNet  MATH  Google Scholar 

  28. Durrett, R., and Schonmann, R.H. (1988) The contact process on a finite set, II. Ann. Prob. 16, 1570–1583

    Article  MathSciNet  MATH  Google Scholar 

  29. Eden, M. (1961) A two dimensional growth process. Pages 223–239 in Vol. IV of the Proceedings of the 4th Berkeley Symposium. U. of California Press, San Francisco

    Google Scholar 

  30. Fine, N.J. (1954) On the asymptotic distribution of certain sums. Proc. AMS. 5, 243–252

    Article  MathSciNet  MATH  Google Scholar 

  31. Fortuin, C.M. and Kastelyn, P.W. (1972) On the random cluster model, I. Introduction and relation to other models. Physica 57, 536–564

    Article  MathSciNet  Google Scholar 

  32. Grimmett, G. (1995) The stochastic random-cluster process and uniqueness of random-cluster measures. Ann. Probab. 24, 1461–1510

    Article  MathSciNet  Google Scholar 

  33. Grimmett, G. (1999) Percolation. Second edition. Springer-Verlag, New York

    MATH  Google Scholar 

  34. Hammersley, J.M. (1959) Bornes supérieures de la probabilité critique dans un process de filtration. Pages 17–37 in Le calcul de probabilités et ses applications. CNRS, Paris

    Google Scholar 

  35. Hammersley, J.M. (1961) The number of polygons on a lattice. Proc. Camb. Phil. Soc. 57, 516–523

    Article  MathSciNet  MATH  Google Scholar 

  36. Hammersley, J.M. and Welsh, D.J.A. (1965) First passage percolation, sub-additive processes, stochastic networks, and generalized renewal theory. In Bernoulli, Bayes, and Laplace. Edited by J. Neyman and L. LeCam. Springer-Verlag, Berlin

    Google Scholar 

  37. Hara, T., and Slade, G. (1989) The triangle condition in percolation. Bull AMS. 21, 269–273

    Article  MathSciNet  MATH  Google Scholar 

  38. Hara, T., and Slade, G. (1990) Mean field critical behaviour for percolation in high dimensions. Comm. Math. Phys. 128, 333–391

    Article  MathSciNet  MATH  Google Scholar 

  39. Hara, T., and Slade, G. (1994) Mean field behaviour and the lace expansion. In Probability and Phase Transition edited by G. Grimmett, Kluwer, Dordrecht

    Google Scholar 

  40. Harris, T.E. (1960) A lower bound for the critical probability in a certain percolation process. Proc. Camb. Phil. Soc. 56, 13–20

    Article  MATH  Google Scholar 

  41. Hunt, G.A. (1957–1958) Markoff processes and potential, I-III. Illinois J. Math. 1, 44–93, 316–319; 2, 151–213

    Google Scholar 

  42. Ishitani, H. (1977) A central limit theorem for the subadditive process and its application to products of random matrices. RIMS, Kyoto 12, 565–575

    Article  MathSciNet  MATH  Google Scholar 

  43. Kac, M. (1946) On the distribution of values of sums of the type E f (2t). Annals of Math. 47, 33–49

    Article  MATH  Google Scholar 

  44. Kalikow, S.A. (1981) Generalized random walk in a random environment. Ann. Prob. 9, 753–768

    Article  MathSciNet  Google Scholar 

  45. Kardar, M., Parisi, G., and Zhang, Y.C. (1986) Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892

    Article  MATH  Google Scholar 

  46. Key, E. (1984) Recurrence and transience for random walk in random environment. Ann. Prob. 12, 529–560

    Article  MathSciNet  MATH  Google Scholar 

  47. Kingman, J.F.C. (1968) The ergodic theory of subadditive processes. J. Roy. Stat. Soc. B 30, 499–510

    MathSciNet  MATH  Google Scholar 

  48. Kingman, J.F.C. (1968) The ergodic theory of subadditive stochastic processes. J. Roy. Stat. Soc. B, 30, 499–510

    MathSciNet  MATH  Google Scholar 

  49. Krug, J. and Spohn, H. (1991) Kinetic roughening of growing surfaces. Pages 479–582 in Solids Far from Equilibrium: Growth, Morphology, and Defects. Cambridge U. Press, Cambridge, UK

    Google Scholar 

  50. Kupiainen, A. (1990) Renormalization group and random systems. Pages 1363–1372 in Proceedings of the International Congress of Math, Kyoto. (1990), Springer-Verlag, New York

    Google Scholar 

  51. Lawler, G. (1991) Intersections of Random Walks. Birkhauser, Boston

    Google Scholar 

  52. LeGall, J.F. (1991) Brownian excursions, trees, and measure valued branching processes. Ann. Prob. 19, 1399–1439

    Article  MathSciNet  Google Scholar 

  53. Licea, C. and Newman, C.M. (1996) Geodesics in two-dimensional first passage percolation. Ann. Prob. 24, 399–410

    Article  MathSciNet  MATH  Google Scholar 

  54. Madras, N., and Slade, G. (1993) Self-Avoiding Random Walk. Birkhauser, Boston

    Google Scholar 

  55. Mountford, T. S. (1993) A metastable result for the finite multi-dimensional contact process. Canad. Math. Bull. 36, 216–222

    Article  MathSciNet  MATH  Google Scholar 

  56. Newman, C.M. (1995) A surface view of first-passage percolation. Pages 1017–1023 in Proceedings of the International Congress of Mathematicians, Berkeley. Birkhäuser, Basel

    Chapter  Google Scholar 

  57. Newman, C.M. and Piza, M.S.T. (1995) Divergence of shape fluctuations in two dimensions. Ann. Probab. 23, 977–1005

    Article  MathSciNet  MATH  Google Scholar 

  58. Newman, C.M., and Schulman, L.S. (1981) Infinite clusters in percolation models. J. Stat. Phys. 26, 613–628

    Article  MathSciNet  MATH  Google Scholar 

  59. Pemantle, R. and Peres, Y. (1994) Planar first passage percolation times are not tight. Pages 261–264 in Probability and Phase Transition, edited by G. Grimmett. Kluwer, Dordrecht.

    Google Scholar 

  60. Port, S. and Stone, C.J. (1969) Potential theory of random walks on Abelian groups. Acta Math. 122, 19–114

    Article  MathSciNet  MATH  Google Scholar 

  61. Richardson, D. (1973) Random growth in a tessellation. Proc. Camb. Phil. Soc. 74, 515–528

    Article  MATH  Google Scholar 

  62. Ritter, G.A. (1976) Random walk in a random environment, critical case. Ph.D. Dissertation, Cornell U.

    Google Scholar 

  63. Russo, L. (1978) A note on percolation Z. fur Wahr. 43, 39–48

    Article  MATH  Google Scholar 

  64. Sawyer, S. (1979) A limit theorem for patch sizes in a selectively neutral immigration model. J. Appl. Prob. 16, 482–495

    Article  MathSciNet  MATH  Google Scholar 

  65. Seymour, P.D., and Welsh, D.J.A. (1978) Percolation probabilities on the square lattice. Ann. Discrete Math. 3, 227–245

    Article  MathSciNet  MATH  Google Scholar 

  66. Smythe, R.T. and Wierman, J.C. (1978) First passage percolation on the square lattice. Lecture Notes in Mathematics 671, Springer-Verlag, Berlin

    MATH  Google Scholar 

  67. Sinai, Y.G. (1982) The limiting behavior of a one-dimensional random walk in a random medium. Th. Prob. Appl. 27, 256–268

    Article  MathSciNet  Google Scholar 

  68. Solomon, F. (1975) Random walks in a random environment. Ann. Prob. 3, 1–31

    Article  MATH  Google Scholar 

  69. Spitzer, F (1962) Hitting probabilities. J. Math. Mech. 11, 593–614

    MathSciNet  MATH  Google Scholar 

  70. Spitzer, F (1964) Principles of Random Walk. Van Nostrand, New York

    MATH  Google Scholar 

  71. Strassen, V. (1964) An invariance principle for the law of the iterated logarithm. Z. fur Wahr. 3, 211–226

    Article  MathSciNet  MATH  Google Scholar 

  72. Sykes, M.F. and Essam, J.W. (1964) Exact critical percolation probabilities for site and bond percolation in two dimensions. J. Math. Phys. 5, 1117–1127

    Article  MathSciNet  Google Scholar 

  73. Wehr, J. and Aizenman, M. (1990) Fluctuations of extensive functions of quenched random couplings. J. Stat. Phys. 60, 287–306

    Article  MathSciNet  MATH  Google Scholar 

  74. Zabolitsky, J.G. and Stauffer, D. (1986a) Simulation of large Eden clusters. Phys. Rev. A 34, 1523–1530

    Article  Google Scholar 

  75. Zabolitsky, J.G. and Stauffer, D. (1986b) Dynamic scaling of Eden cluster surfaces. Phys. Rev. Letters 57, 1809

    Article  Google Scholar 

  76. Harry Kesten (with J. Th. Runnenberg) Priority in waiting line problems. Proc. Koninklijke Nederlandse Akad. van Wetenschappen, Ser. A. 60(1957), 312–336

    MathSciNet  Google Scholar 

  77. Harry Kesten Accelerated stochastic approximation. Ann. Math. Stat. 29(1958), 41–59

    Article  MathSciNet  MATH  Google Scholar 

  78. Harry Kesten (with M. Kac) On rapidly mixing transformations and an application to continued fractions. Bulletin AMS. 64(1958), 283–287

    Article  MATH  Google Scholar 

  79. Harry Kesten Symmetric random walks on groups. Trans. AMS 92(1959), 336–354

    Article  MathSciNet  MATH  Google Scholar 

  80. Harry Kesten Full Banach mean values on countable groups. Math. Scand. 7(1959), 146–156

    MathSciNet  MATH  Google Scholar 

  81. Harry Kesten (with N. Morse) A property of the multinomial distribution. Ann. Math. Stat. 30(1959), 120–127

    Article  MathSciNet  MATH  Google Scholar 

  82. Harry Kesten On a series of cosecants II. Proc. Koninklijke Nederlandse Akad. van Wetenschappen, Ser. A. 62 (1959), 110–119

    MathSciNet  MATH  Google Scholar 

  83. Harry Kesten Uniform distributions mod 1. Annals of Math. 71(1960), 445–471

    Article  MathSciNet  MATH  Google Scholar 

  84. Harry Kesten H. Furstenberg Products of random matrices. Ann. Math. Stat. 31(1960), 457–469

    Article  MathSciNet  MATH  Google Scholar 

  85. Harry Kesten Some remarks on the capacity of compound channels in the semi-continuous case. Information and Control. 4(1961), 169–184

    Article  MathSciNet  MATH  Google Scholar 

  86. Harry Kesten On a theorem of Spitzer and Stone and random walks with absorbing barriers. Illinois J. Math. 5(1961), 246–262

    MathSciNet  MATH  Google Scholar 

  87. Harry Kesten Random walks with absorbing barriers and Toeplitz forms. Illinois J. Math. 5(1961), 267–290

    MathSciNet  MATH  Google Scholar 

  88. Harry Kesten Uniform distributions mod 1, II. Acta Arithmetica. 7 (1962), 355–380

    MathSciNet  MATH  Google Scholar 

  89. Harry Kesten Some probabilistic theorems on diophantine approximation. Trans. AMS. 103(1962), 189–217

    Article  MathSciNet  MATH  Google Scholar 

  90. Harry Kesten (with Z. Ciesielski) A limit theorem for the fractional parts of the sequence 2k t. Proc. AMS. 13(1962), 596–600

    MathSciNet  MATH  Google Scholar 

  91. Harry Kesten Occupation times for Markov and semi-Markov chains. Trans. AMS. 103(1962), 82–112

    Article  MathSciNet  MATH  Google Scholar 

  92. Harry Kesten (with D. Ornstein and F. Spitzer) A general property of random walk. Bulletin AMS 68(1962), 526–528

    Article  MathSciNet  MATH  Google Scholar 

  93. Harry Kesten On extreme eigenvalues of translation kernels and Toeplitz matrices. J. d’Analyse Math. 10 (1962/63), 117–138

    Google Scholar 

  94. Harry Kesten Positivity intervals of stable processes. J. Math. Mech. 12(1963), 391–410

    MathSciNet  MATH  Google Scholar 

  95. Harry Kesten (with F. Spitzer) Ratio theorems for random walks, I. J. d’Analyse Math. 11(1963), 285–322

    Article  MathSciNet  MATH  Google Scholar 

  96. Harry Kesten Ratio theorems for random walks, II. J. d’Analyse Math. 11 (1963), 323–379

    Article  MathSciNet  MATH  Google Scholar 

  97. Harry Kesten On the number of self-avoiding walks. J. Math. Phys. 4(1963), 960–969

    Article  MathSciNet  MATH  Google Scholar 

  98. Harry Kesten On the number of self-avoiding walks, II. J. Math. Phys. 5 (1964), 1128–1137

    Article  MathSciNet  MATH  Google Scholar 

  99. Harry Kesten The discrepancy of random sequences kx Acta Arithmetica 10 (1964), 183–213

    MathSciNet  MATH  Google Scholar 

  100. Harry Kesten An iterated logarithm law for local time. Duke Math. J. 32(1965), 447–456

    Article  MathSciNet  MATH  Google Scholar 

  101. Harry Kesten (with F. Spitzer) Random walks on countably infinite Abelian groups. Acta Mathematica 114(1965), 237–265

    Article  MathSciNet  MATH  Google Scholar 

  102. Harry Kesten (with B.P. Stigum) A limit theorem for multidimensional Galton-Watson processes. Ann. Math. Stat. 37(1966), 1211–1223

    Article  MathSciNet  MATH  Google Scholar 

  103. Harry Kesten (with B.P. Stigum) Additional limit theorems for indecomposable multidimensional Galton-Watson processes. Ann. Math. Stat. 37(1966), 1463–1481

    Article  MathSciNet  MATH  Google Scholar 

  104. Harry Kesten (with V.T. Sós) On two problems of Erdös, Szüs, and Turân concerning diophantine approximations. Acta Arithmetica 12(1966), 183–192

    MathSciNet  MATH  Google Scholar 

  105. Harry Kesten On a conjecutre of Erdös and Szüs related to uniform distribution mod 1. Acta Arithmetica 12(1966), 193–212

    MathSciNet  MATH  Google Scholar 

  106. Harry Kesten (with P. Ney and F. Spitzer) The Galton-Watson process with mean one and finite variance. Teorija Verojatnostei i ee Primenenija 11(1966), 579–611

    MathSciNet  MATH  Google Scholar 

  107. Harry Kesten The Martin boundary of recurrent random walks on countable groups. Proc. 5th Berkeley Symposium on Math. Stat. and Prob., Vol. II, Part 2 (1967), 51–74

    Google Scholar 

  108. Harry Kesten (with B.P. Stigum) Limit theorems for decomposable multidimensional Galton-Watson processes. J. Math. Anal. Appl. 7(1967), 309–338

    Article  MathSciNet  Google Scholar 

  109. Harry Kesten A Tauberian theorem for random walk. Israel J. Math. 6(1968), 279–294

    Article  MathSciNet  MATH  Google Scholar 

  110. Harry Kesten A sharper form of the Doeblin-Lévy-Kolmogorov-Rogozin inequality for concentration functions. Math. Scand. 25(1969), 133–144

    MathSciNet  MATH  Google Scholar 

  111. Harry Kesten A convolution equation and hitting probabilities of single points for processes with stationary independent increments. Bulletin AMS. 75(1969), 573–578

    Article  MathSciNet  MATH  Google Scholar 

  112. Harry Kesten Hitting probabilities of single points for processes with stationary independent increments. Memoirs of the AMS, No. 93, (1969)

    Google Scholar 

  113. Harry Kesten A ratio limit theorem for symmetric random walk. J. d’Analyse Math. 23(1970), 199–213

    Article  MathSciNet  MATH  Google Scholar 

  114. Harry Kesten Hitting of sets by processes with stationary independent increments. Proc. Int. Cong. Math., Nice (1970) Gauthier-Villar, Paris

    Google Scholar 

  115. Harry Kesten Quadratic transformations: A model for population growth. Adv. Appl. Prob. 2 (1970), 1–82 and 179–228

    Google Scholar 

  116. Harry Kesten The limit points of a normalized random walk. Ann. Math. Stat. 41(1970), 1173–1205

    Article  MathSciNet  MATH  Google Scholar 

  117. Harry Kesten Some nonlinear stochastic growth models. Bulletin AMS. 77(1971), 492–551

    Article  MathSciNet  MATH  Google Scholar 

  118. Harry Kesten (with R.K. Getoor) Continuity of local times for Markov processes. Compositio Math. 24(1972), 277–303

    MathSciNet  MATH  Google Scholar 

  119. Harry Kesten (with B.P. Stigum) Balanced growth under uncertainty in decomposable models. Pages 339–381 in Essays on Economic Behavior under Uncertainty. Edited by M.S. Balch, D.L. McFadden, and S.Y. Wu. (1974) American Elsevier, New York

    Google Scholar 

  120. Harry Kesten Sums of independent random variables–without moment conditions. Ann. Math. Stat. 43(1972), 701–732

    Article  MathSciNet  MATH  Google Scholar 

  121. Harry Kesten Limit theorems for stochastic growth models. Adv. Appl. Prob. 4 (1972), 193–232 and 393–428

    Google Scholar 

  122. Harry Kesten Renewal theory for functionals of a Markov chain with general state space. Ann. Prob. 2(1974), 355–386

    Article  MathSciNet  MATH  Google Scholar 

  123. Harry Kesten Random difference equations and renewal theory for products of random matrices. Acta Mathematica. 131(1973), 208–248

    Article  MathSciNet  Google Scholar 

  124. Harry Kesten (with K.B. Erickson) Strong and weak points of a normalized random walk. Ann. Prob. 2(1974), 553–579

    Article  MathSciNet  MATH  Google Scholar 

  125. Harry Kesten (with F. Spitzer) Controlled Markov chains. Ann. Prob. 3(1975), 32–40

    Article  MathSciNet  MATH  Google Scholar 

  126. Harry Kesten Sums of stationary sequences cannot grow slower than linearly. Proc. AMS. 49(1975), 205–211

    Article  MathSciNet  MATH  Google Scholar 

  127. Harry Kesten Lévy processes with nowhere dense range. Indiana Math. J. 25(1976), 45–64

    Article  MathSciNet  MATH  Google Scholar 

  128. Harry Kesten (with M.V. Kozlov and F. Spitzer) A limit law for random walk in a random in a random environment. Comp. Math. 30(1975), 145–168

    MathSciNet  MATH  Google Scholar 

  129. Harry Kesten Existence and uniqueness of countable one dimensional Markov random fields. Ann. Prob. 4(1976), 557–569

    Article  MathSciNet  MATH  Google Scholar 

  130. Harry Kesten Recurrence criteria for multi-dimensional Markov chains and multi-dimensional linear birth and death processes. Adv. Appl. Prob. 8(1976), 58–87

    Article  MathSciNet  MATH  Google Scholar 

  131. Harry Kesten (with G.L. O’Brien) Examples of mixing sequences. Duke Math. J. 43(1976) 405–415

    Article  MathSciNet  MATH  Google Scholar 

  132. Harry Kesten A renewal theorem for random walk in random environment. Pages 67–77 in Proc. Symp. Pure Math. 31, (1977) American Math. Society, Providence, RI

    Google Scholar 

  133. Harry Kesten Erickson’s conjecture on the rate of escape of d-dimensional random walk. Trans. AMS 240(1978), 65–113

    MathSciNet  MATH  Google Scholar 

  134. Harry Kesten The speed of convergence of a martingale. Israel Math. J. 32(1979), 83–96

    Article  MathSciNet  MATH  Google Scholar 

  135. Harry Kesten (with G. Papanicolaou) A limit theorem for turbulent diffusion. Comm. Math. Phys. 65(1979), 97–128

    Article  MathSciNet  MATH  Google Scholar 

  136. Harry Kesten Positive harmonic functions. Proc. Symp. Pure Math. 35, part I, (1979) American Math. Society, Providence, RI

    Google Scholar 

  137. Harry Kesten (with F. Spitzer) A limit theorem related to a new class of self-similar processes. Z fur Wahr. 50(1979), 5–25

    Article  MathSciNet  MATH  Google Scholar 

  138. Harry Kesten On the time constant and path length of first-passage percolation. Adv. Appl. Prob. 12(1980), 848–863

    Article  MathSciNet  MATH  Google Scholar 

  139. Harry Kesten (with G. Papanicolaou) A limit theorem for stochastic acceleration. Comm. Math. Phys. 78(1980), 19–63

    Article  MathSciNet  MATH  Google Scholar 

  140. Harry Kesten The number of alleles in electrophoretic experiments. Theor. Pop. Biol. 18(1980), 290–294

    Article  MathSciNet  MATH  Google Scholar 

  141. Harry Kesten The number of distinguishable alleles according to the Ohta-Kimura model of neutral mutation. J. Math. Biol. 10, 167–187

    Google Scholar 

  142. Harry Kesten The critical probability for bond percolation on the square lattice equals 1/2. Comm. Math. Phys. 74(1980), 41–59

    Article  MathSciNet  MATH  Google Scholar 

  143. Harry Kesten Random processes in random enviornments. Pages 82–92 in the proceedings of Models of biological growth and spread. Springer Lecture Notes in Biomathematics, Vol. 38, Springer-Verlag, NY

    Google Scholar 

  144. Harry Kesten (with Y. Ogura) Recurrence properties of Lotka-Volterra models with random fluctuations. J. Math. Soc. Japan. 32(1981), 335–366

    Article  MathSciNet  Google Scholar 

  145. Harry Kesten (with J.T. Cox) On the continuity of the time constant of first-passage percolation. J. Appl. Prob. 18(1981), 809–819

    Article  MathSciNet  MATH  Google Scholar 

  146. Harry Kesten Analyticity properties and power estimates of functions in percolation theory. J. Stat. Phys. 25(1981), 717–756

    Article  MathSciNet  MATH  Google Scholar 

  147. Harry Kesten Percolation Theory for Mathematicians. (1982) Birkhéuser, Boston

    Google Scholar 

  148. Harry Kesten Percolation theory and resistance of random elctrical networks. Proc. Int. Cong. Math., Warsaw, (1983), Vol. 2, 1081–1088

    Google Scholar 

  149. Harry Kesten (with G. Grimmett) First-passage percolation, network flows and electrical resistances. Z. fur Wahr. 66(1984), 335–366

    Article  MathSciNet  MATH  Google Scholar 

  150. Harry Kesten (with G. Grimmett) Random electrical networks and complete graphs. J. London Math. Soc., Series 2.30 (1984), 171–192

    Google Scholar 

  151. Harry Kesten (with F. Spitzer) Convergence in distribution of products of random matrices. Z fur Wahr. 67(1984), 363–386

    Article  MathSciNet  MATH  Google Scholar 

  152. Harry Kesten (with K. Kawazu) On birth and death processes in symmetric random environments. J. Stat. Phys. 37(1984), 561–576

    Article  MathSciNet  MATH  Google Scholar 

  153. Harry Kesten Aspects of first passage percolation. Pages 126–264 in École d’Été de Probabilités de Saint Flour XIV, (1984), Lecture Notes in Mathematics, 1180, Springer-Verlag, New York

    Google Scholar 

  154. Harry Kesten (with J. van den Berg) Inequalities with application to percolation and reliability. J. Appl. Prob. 22(1985), 556–569

    Article  MathSciNet  MATH  Google Scholar 

  155. Harry Kesten First-passage percolation and a higher generalization. Pages 235–251 in Particle Systems, Random Media and Large Deviaitons. Contemporary Math., Vol. 41, American Mathematical Society, Providence, RI

    Google Scholar 

  156. Harry Kesten The incipient infinite cluster in two-dimensional percolation. Prob. Th. Rel. Fields. 73(1986), 369–394

    Article  MathSciNet  MATH  Google Scholar 

  157. Harry Kesten Subdiffusive behavior of a random walk on a random cluster. Ann. Inst. H. Poincaré 22(1986), 425–487

    MathSciNet  MATH  Google Scholar 

  158. Harry Kesten Random walks on random clusters at criticality. Pages 211–218 in Probabilistic Mathods in Math. Physics, edited by K. Itô and N. Ikeda. (1987) Kinokunyia Co., Ltd.

    Google Scholar 

  159. Harry Kesten The limit distribution of Sinai’s random walk in random environment. Physica A. 138(1986), 299–309

    Article  MathSciNet  MATH  Google Scholar 

  160. Harry Kesten Comment on “Evidence for Ising-type critical phenomena in two-dimensional percolation.” Phys. Rev. Leu. 56 (1986), 1210

    Article  Google Scholar 

  161. Harry Kesten The influence of Mark Kac on probability. Ann. Prob. 14(1986), 1103–1128. Correction in Ann. Prob. 15(1987), 1228

    Google Scholar 

  162. Harry Kesten Surfaces with minimal random weights and maximal flows: a higher dimensional generalization of first passage percolation. Illinois. J. Math. 31 (1987), 99–166

    MathSciNet  MATH  Google Scholar 

  163. Harry Kesten (with M. Aizenman and C.M. Newman) Uniqueness of the infinite cluster and related results in percolation. Pages 13–20 in Percolation Theory and Ergodic Theory of Infinite Particle Systems. IMA Volumes in Math. Appl., Vol. 8, (1987), Springer-Verlag, New York

    Google Scholar 

  164. Harry Kesten A scaling relation at criticality for 2D-percolation. Pages 203–212 in Percolation Theory and Ergodic Theory of Infinite Particle Systems. IMA Volumes in Math. Appl., Vol. 8, (1987), Springer-Verlag, New York

    Google Scholar 

  165. Harry Kesten Scaling relations for 2D-percolation. Comm. Math. Phys. 109(1987), 109–156

    Article  MathSciNet  MATH  Google Scholar 

  166. Harry Kesten (with M. Aizenman and C.M. Newman) Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Comm. Math. Phys. 111(1987), 505–531

    Article  MathSciNet  MATH  Google Scholar 

  167. Harry Kesten (with Y. Zhang) Strict inequalities for some critical exponents in 2D-percolation. J. Stat. Phys. 46(1987), 1031–1055

    Article  MathSciNet  MATH  Google Scholar 

  168. Harry Kesten How long are the arms in DLA? J. Phys. A. 20 (1987), L29–L33

    Article  MathSciNet  Google Scholar 

  169. Harry Kesten Hitting probabilities of random walks on Zd. Stoch. Proc. and Appl. 25(1987), 165–184

    Article  MathSciNet  MATH  Google Scholar 

  170. Harry Kesten Percolation theory and first-passage percolation. Ann. Prob. 15(1987), 1231–1271

    Article  MathSciNet  MATH  Google Scholar 

  171. Harry Kesten (with J.T.Bendler, M.Dishon and G.H.Weiss) A first passage time problem for random walk occupancy. J. Stat. Phys. 50(1988), 1069–1087

    Article  MathSciNet  MATH  Google Scholar 

  172. Harry Kesten (with J.T.Chayes, L.Chayes, G.Grimmett, R.Schonmann) The correlation length for the high density phase of Bernoulli percolation. Ann. Prob. 17 (1989) 1277–1302

    Article  MathSciNet  MATH  Google Scholar 

  173. Harry Kesten Recent results in rigorous percolation theory. Pages 217–232 in Colloque Paul Lévy sur les Processus Stochastiques, Astérisque, Paris vol. 157/158, (1988)

    Google Scholar 

  174. Harry Kesten with J.Bricmont, J.Lebowitz and R.Schonmann) A note on the large dimensional Ising model. Comm. Math. Phys. 122(1989), 597–607

    Article  MathSciNet  MATH  Google Scholar 

  175. Harry Kesten (with R.Schonmann) Behavior in large dimensions of the Potts and Heisenberg model. Rev. in Math. Phys. 1(1990), 147–182

    Article  MathSciNet  Google Scholar 

  176. Harry Kesten Correlation length and critical probabilities of slabs for percolation, unpublished preprint, 1988.

    Google Scholar 

  177. Harry Kesten Asymptotics in high dimensions for percolation. Pages 219–240 in Disorder in Physical Systems, (1990) edited by G. Grimmett and D.J.A. Welsh, Oxford Univ. Press, Oxford, UK

    Google Scholar 

  178. Harry Kesten Asymptotics in high dimensions for the Fortuin-Kasteleyn random cluster model. Pages 57–85 in Spatial Stochastic Processes, (1992), edited by K.S. Alexander and J.C. Watkins, Birkhäuser, Boston

    Google Scholar 

  179. Harry Kesten (with R. Durrett) The critical parameter for connectedness of some random graphs. Pages 161–176 in A Tribute to Paul Erds, (1990) edited by A. Baker, B. Bollobas and A. Hajnal, Cambridge Univ. Press, Cambridge, UK

    Google Scholar 

  180. Harry Kesten (with Y. Zhang) The probability of a large finite cluster in supercritical Bernoulli percolation. Ann. Prob. 18(1990), 537–555

    Article  MathSciNet  MATH  Google Scholar 

  181. Harry Kesten Supercritical branching processes with countably many types and the size of random Cantor sets. Pages 103–121 in Probability, Statistics and Mathematics, Papers in honor of Samuel Karlin, (1989) edited by T.E. Anderson and K. Athreya, Academic Press, Orlando, FL

    Google Scholar 

  182. Harry Kesten (with R. Durrett and E. Waymire) On weighted heights of random trees, J. Theoret. Prob. 4(1991), 223–237

    Article  MathSciNet  MATH  Google Scholar 

  183. Harry Kesten Connectivity of certain graphs on halfspaces, quarter spaces,—, Pages 91–104 in Probability Theory, 1992 edited by L.H.Y. Chen, K.P. Choi, K. Hu and J-H. Lou, Walter de Gruyter & Co, Berlin

    Google Scholar 

  184. Harry Kesten Upper bounds for the growth rate of DLA, Physica A 168 (1990), 529–535

    Article  MathSciNet  Google Scholar 

  185. Harry Kesten (with R. Durrett and G. Lawler) Making money from fair games. Pages 255–267 in Random walk, Brownian motion and interacting particle systems (1991), edited by R. Durrett and H. Kesten, Birkhéuser, Boston

    Google Scholar 

  186. Harry Kesten (with G. Lawler) A necessary condition for making money from fair games. Ann. Prob. 20(1992), 855–882.

    Article  MathSciNet  MATH  Google Scholar 

  187. Harry Kesten Relations between solutions to a discrete and continuous Dirichlet problem. Pages 309–321 in Random walk, Brownian motion and interacting particle systems (1991), edited by R. Durrett and H. Kesten, Birkhäuser, Boston

    Google Scholar 

  188. Harry Kesten Some caricatures of multiple contact diffusion-limited aggregation and the eta-model. Pages 179–227 in Stochastic Analysis (1991), edited by M.T. Barlow and N.H. Bingham, Cambridge Univ. Press, Cambridge, UK

    Google Scholar 

  189. Harry Kesten (with R. Mailer) Ratios of trimmed sums and order statistics. Ann. Prob. 20(1992), 1805–1842

    Article  MathSciNet  MATH  Google Scholar 

  190. Harry Kesten (with R. Maller) Infinite limits and infinite limit points of random walks and trimmed sums. Ann. Prob. 22(1994), 1473–1513

    Article  MathSciNet  MATH  Google Scholar 

  191. Harry Kesten (with J. van den Berg) Inequalities for the time constant in first-passage percolation. Ann. Appl. Prob. 3(1993), 56–80

    Article  MathSciNet  MATH  Google Scholar 

  192. Harry Kesten On the speed of convergence in first-passage percolation, Ann. Appl. Prob. 3(1993), 296–338

    Article  MathSciNet  MATH  Google Scholar 

  193. Harry Kesten An absorption problem for several Brownian motions. Pages 59–72 in Seminar on Stochastic Processes 1991, Birkhäuser, Boston

    Google Scholar 

  194. Harry Kesten (with G. R. Grimmett and Y. Zhang) Random walk on the infinite cluster of the percolation model. Prob. Th. Rel. Fields 96(1993), 33–44

    Article  MathSciNet  MATH  Google Scholar 

  195. Harry Kesten (with C. E. Bezuidenhout and G. R. Grimmett) Strict inequality for critical values of Potts models and random cluster processes, Comm. Math. Phys. 158(1993), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  196. Harry Kesten (with J. T. Cox, A. Gandolfi and P. Griffin) Greedy lattice animals I. Upper bounds. Ann. Appl. Prob. 3(1993), 1151–1169

    Article  MathSciNet  MATH  Google Scholar 

  197. Harry Kesten (with A. Gandolfi) Greedy lattice animals II: Linear growth. Ann. Appl. Prob. 4(1994), 76–107

    Article  MathSciNet  MATH  Google Scholar 

  198. Harry Kesten (with Y. Zhang) The tortuosity of occupied crossings of a box in critical percolation. J. Stat. Phys. 70(1993), 599–611

    Article  MathSciNet  MATH  Google Scholar 

  199. Harry Kesten First-and last-passage percolation. Proceedings of a Statistics Conference in Rio de Janeiro, Brasil, July 1992

    Google Scholar 

  200. Harry Kesten Convergence in distribution of lightly trimmed and untrimmed sums are equivalent. Math. Proc. Camb. Phil. Soc. 113(1993), 615–638

    Article  MathSciNet  MATH  Google Scholar 

  201. Harry Kesten A limit theorem for weighted branching process trees. Pages 153–166 in The Dynkin Festschrift. Markov Processes and their Applications, (1994), edited by M. I. Freidlin, Birkhäuser, Boston

    Google Scholar 

  202. Harry Kesten Frank Spitzer’s work on random walk and Brownian motion. Ann. Prob. 21(1993), 593–607

    Article  MathSciNet  MATH  Google Scholar 

  203. Harry Kesten (with R. A. Mailer) The effect of trimming on the law of large numbers and generalized laws of the iterated logarithm. Proc. London Math. Soc. 71(1995), 441–480

    Article  MathSciNet  MATH  Google Scholar 

  204. Harry Kesten (with P. A. Ferrari, S. Martinez and P. Picco) Existence of quasi stationary distributions. A renewal dynamical approach, Ann. Prob. 23(1995), 501–521

    Article  MathSciNet  MATH  Google Scholar 

  205. Harry Kesten (with I. Benjamini) Percolation of arbitrary words in (0, 11N, Ann. Prob. 23(1995), 1024–1060

    Article  MathSciNet  MATH  Google Scholar 

  206. Harry Kesten (with R. A. Mailer) Random deletion does not affect asymptotic normality or quadratic negligibility. J. Multivariate Anal. 63(1997), 136–179

    Article  MathSciNet  MATH  Google Scholar 

  207. Harry Kesten A ratio limit theorem for (sub)Markov chains on (1, 2,…) with bounded jumps. Adv. Appl. Prob. 27(1995), 652–691

    Article  MathSciNet  MATH  Google Scholar 

  208. Harry Kesten (with R. Schonmann) On some growth models with a small parameter. Prob. Th. Rel. Fields. 101(1995), 435–468

    Article  MathSciNet  MATH  Google Scholar 

  209. Harry Kesten (with Boris Pittel) A local limit theorem for the number of nodes, the height and the number of final leaves in critical branching process trees. Random Structures & Algorithms 8(1996), 243–299

    Article  MathSciNet  MATH  Google Scholar 

  210. Harry Kesten Branching random walk with a critical branching part. J. Theoret. Prob. 8(1995), 921–962

    Article  MathSciNet  MATH  Google Scholar 

  211. Harry Kesten (with P. Ferrari and S. Martinez) R-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata. Ann. Appl. Prob. 6(1996), 577–616

    Article  MathSciNet  MATH  Google Scholar 

  212. Harry Kesten (with Sungchul Lee) The central limit theorem for weighted minimal spanning trees on random points. Ann. Appl. Prob. 6(1996), 495–527

    Article  MathSciNet  MATH  Google Scholar 

  213. Harry Kesten (with I. Benjamini) Distinguishing sceneries by observing the scenery along a random walk path. J. d’Analyse Math. 69(1996), 97–135

    Article  MathSciNet  MATH  Google Scholar 

  214. Harry Kesten Detecting a single defect in a scenery by observing the scenery along a random walk path. Pages 117–183 in Itü’s Stochastic Calculus and Probability Theory, (1996), edited by N. Ikeda, S. Watanabe, M. Fukushima and H. Kunita, Springer-Verlag, New York

    Google Scholar 

  215. Harry Kesten On the non-convexity of the time constant in first-passage percolation, Electronic Comm. Probab. 1 (1996) 1–6; http://www.math.washington.edu/ejpecp

    MathSciNet  MATH  Google Scholar 

  216. Harry Kesten (with R. A. Mailer) Two renewal theorems for general random walks tending to infinity. Prob. Th. Rel. Fields 106(1996), 1–38

    Article  MathSciNet  MATH  Google Scholar 

  217. Harry Kesten (with Y. Zhang) A central limit theorem for “critical” first-passage percolation in two dimensions. Prob. Th. Rel. Fields 107(1997), 137–160

    Article  MathSciNet  MATH  Google Scholar 

  218. Harry Kesten A universal form of the Chung-type law of the iterated logarithm. Ann. Prob. 25(1997), 1588–1620

    Article  MathSciNet  MATH  Google Scholar 

  219. Harry Kesten (with R. A. Mailer) Divergence of a random walk through deterministic and random subsequences. J. Theoret. Prob. 10(1997) 395–427

    Article  MathSciNet  MATH  Google Scholar 

  220. Harry Kesten (with R. A. Mailer) Random walks crossing high level curved boundaries. J. Theoret. Prob. 11(1998), 1019–1074

    Article  MathSciNet  MATH  Google Scholar 

  221. Harry Kesten (with R. A. Mailer) Random walks crossing power law boundaries. Studia Sci. Math. Hungarica. 34(1998), 219–252

    MathSciNet  MATH  Google Scholar 

  222. Harry Kesten Distinguishing and reconstructing sceneries from observations along random walk paths, in DIMACS series in Discrete Math and Computer Science

    Google Scholar 

  223. Harry Kesten (with C. Borgs, J. T. Chayes and J. Spencer) Uniform boundedness of critical crossing probabilities implies hyperscaling, in preparation

    Google Scholar 

  224. Harry Kesten (with V. Sidoravicius and Y. Zhang) Almost all words are seen in critical site percolation on the triangular lattice. Electronic J. Prob.* 3 (1998), paper 10

    Google Scholar 

  225. Harry Kesten (with J. van den Berg) Asymptotic density in a coalescing random walk model. Preprint

    Google Scholar 

  226. Harry Kesten (with Z.G. Su) Asymptotic behavior of the critical probability of for ρ-percolation in high dimension. Preprint

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Rick Durrett

Authors
  1. Rick Durrett
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Maury Bramson

  2. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Rick Durrett

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Birkhäuser Boston

About this chapter

Cite this chapter

Durrett, R. (1999). Harry Kesten’s Publications. In: Bramson, M., Durrett, R. (eds) Perplexing Problems in Probability. Progress in Probability, vol 44. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2168-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2168-5_1

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7442-1

  • Online ISBN: 978-1-4612-2168-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation