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References
R. Ahlberg and S. Janson (1984). Upper bounds for the connectivity constant, preprint, Uppsala Univ.
M. Aizenman, J.T. Chayes, L. Chayes, J. Fröhlich and L. Russo (1983). On a sharp transition from area law to perimeter law in a system of random surfaces, Comm. Math. Phys. 92, 19–69.
J. van den Berg and H. Kesten (1985). Inequalities with applications to percolation and reliability, to appear in J. Appl. Prob.
L. Breiman (1968). Probability, Addison-Wesley Publ. Co.
M. Campanino and L. Russo (1985). An upper bound on the critical percolation probability for the three-dimensional cubic lattice, to appear in Ann. Probab.
J.T. Cox (1980). The time constant of first-passage percolation on the square lattice, Adv. Appl. Prob. 12, 864–879.
J.T. Cox and R. Durrett (1981). Some limit theorems for percolation processes with necessary and sufficient conditions, Ann. Probab. 9, 583–603.
J.T. Cox and R. Durrett (1983). Oriented percolation in dimension d≥4: bounds and asymptotic formulas, Math. Proc. Comb. Phil. Soc. 93, 151–162.
J.T. Cox and H. Kesten (1981). On the continuity of the time constant of first-passage percolation, J. Appl. Prob. 18, 809–819.
C. Dellacherie and P.A. Meyer (1975). Probabilités et potential, Ch. I–IV, Hermann.
M. Donsker and S.R.S. Varadhan (1975). Asymptotics of the Wiener sausage, Comm. Pure Appl. Math. 28, 525–565.
J. Dugundji (1966). Topology, Allyn and Bacon, Inc.
R. Durrett (1984). Oriented percolation in two dimensions, Ann. Probab. 12, 999–1040.
R. Durrett and T.M. Liggett (1981). The shape of the limit set in Richardson's growth model, Ann. Probab. 9, 186–193.
M. Eden (1961). A two dimensional growth process, Proc. Fourth Berkeley Symp. Math. Stat. Prob., Vol IV, 223–239, Univ. of Cal. Press.
D.R. Fulkerson (1975). Flow networks and combinational operations research pp. 139–171 in Studies in graph theory, D.R. Fulkerson ed., Math. Assoc. of America.
G. Grimmett and H. Kesten (1984). First-passage percolation, network flows and electrical resistances, Z. Wahrsch. verw. Geb. 66, 335–366.
J.M. Hammersley (1974). Postulates for subadditive processes, Ann. Probab. 2, 652–680.
J.M. Hammersley and D.J.A. Welsh (1965). First-passage perco-colation, subadditive processes, stochastic networks and genralized renewal theory, pp. 61–110 in Bernoulli, Bayes, Laplace Anniversary Volume, J. Neyman and L.M. LeCam eds. Springer-Verlag.
T.E. Harris (1960). A lower bound for the critical probability in a certain percolation process, Proc. Cambr. Phil. Soc. 56, 13–20.
S. Janson (1981). An upper bound for the velocity of first-passage percolation, J. Appl. Prob. 18, 256–262.
H. Kesten (1980). On the time constant and path length of first-passage percolation, Adv. Appl. Prob. 12, 848–863.
H. Kesten (1982). Percolation theory for mathematicians, Birkhäuser-Boston.
H. Kesten (1984). Surfaces with minimal random weights and maximal flows: a higher dimensional version of first-passage percolation, preprint.
J.F.C. Kingman (1973). Subadditive ergodic theory, Ann. Probab. 1, 883–909.
J.F.C. Kingman (1975). Subadditive processes, pp. 168–223 in Lecture Notes in Mathematics, Vol. 539, Springer-Verlag.
T.M. Liggett (1985). An improved subadditive ergodic theorem, Ann. Probab. 13.
D. Richardson (1973). Random growth in a tesselation, Proc. Cambr. Phil. Soc. 74, 515–528.
H.P. Rosenthal (1970). On the subspaces of Lp(p>2) spanned by sequences of independent random variables, Isr. J. Math. 8, 273–303.
R.T. Smythe (1980). Percolation models in two and three dimensions, pp. 504–511 in Biological Growth and Spread, Lecture Notes in Biomath., Vol 38, Springer-Verlag.
R.T. Smythe and J.C. Wierman (1978). First-passage percolation on the square lattice, Lecture Notes in Mathematics, Vol. 671, Springer-Verlag.
E.H. Spanier (1966). Algebraic topology, McGraw-Hill.
H. Whitney (1932). Non-separable planar graphs, Trans. Amer. Math. Soc. 34, 339–362.
H. Whitney (1933). Planar graphs, Fund. Math. 21, 73–84.
J.C. Wierman (1980). Weak moment conditions for time coordinates in first-passage percolation models, J. Appl. Prob. 17, 968–978.
J.C. Wierman and W. Reh (1978). On conjectures in first-passage percolation theory, Ann. Probab. 6, 388–397.
Y. Zhang and Y.C. Zhang (1984). A limit theorem for Non/n in first-passage percolation, Ann. Probab. 12, 1068–1076.
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Kesten, H. (1986). Aspects of first passage percolation. In: Hennequin, P.L. (eds) École d'Été de Probabilités de Saint Flour XIV - 1984. Lecture Notes in Mathematics, vol 1180. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0074919
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DOI: https://doi.org/10.1007/BFb0074919
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