Abstract
In the early sixties György Pólya gave a talk in Budapest where he told the following story.
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References
P. Auer and P. Révész, On the relative frequency of points visited by random walk on ℤ2, Coll. Math. Soc. J. Bolyai, 57, Limit theorems in probability and Statistics (1990), 27–33.
P. Bártfai, Die Bestimmung der zu einem wiederkehrenden Prozess gehörenden Verteilungsfunktion aus den mit Fehlern behafteten Daten einer Einzigen Realisation, Studia Sei. Math. Hung., 1 (1966), 161–168.
Bass and Griffin, The most visited site of Brownian motion and simple random walk, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 70 (1985), 417–436.
B. Bollobás, Random Graphs, Academic Press, London, 1985.
B. Bollobás, T. I. Fenner and A. M. Frieze, An algorithm for finding Hamiltonian paths and cycles in random graphs, Combinatorica, 7 (1987), 327–342.
K.-L. Chung and P. Erdős, On the application of the Borel-Cantelli lemma, Trans. Amer. Math. Soc, 72 (1952), 179–186.
K.-L. Chung, P. Erdős and T. Sirao, On the Lipschitz condition for Brownian motion, J. Math. Soc. Japan, 11 (1959), 263–274.
E. Csáki, P. Erdős and P. Révész, On the length of the longest excursion, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 68 (1985), 365–382.
E. Csáki, A. Földes and J. Komlós, Limit theorems for Erdős-Rényi type problems, Studia Sei. Math. Hung., 22 (1987), 231–232.
M. Csörgő, A glimpse of the impact of Pál Erdős on probability and statistics, The Canadian Journal of Statistics, 30 (2002), 493–556.
M. Csörgő and J. Steinebach, Improved Erdős-Rényi and strong approximation laws for increments of partial sums, Ann. Probab., 9 (1981), 988–996.
S. Csörgő, Erdős-Rényi laws, Ann. Statist, 7 (1979), 772–787.
P. Deheuvels, P. Erdős, K. Grill and P. Révész, Many heads in a short block, Math. Stat, and Probab. Th. Proc. of the 6th Pannonian Symp. Vol. A (1986), 53–67.
A. Dembo, Y. Peres, J. Rosen and O. Zeitouni, Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk, Acta Math, (to appear).
A. Dvoretzky and P. Erdős, Some problems on random walk in space, Proc. Second Berkeley Symposium (1950), 353–368.
A. Dvoretzky, P. Erdős and S. Kakutani, Nonincrease everywhere of the Brownian motion process, Proc. 4th Berkeley Sympos. Math. Statist, and Probab. Vol II. (1961), 103–116. Univ. California Press, Berkeley.
F. Eggenberger and G. Pólya, Über die Statistik verketteter Vorgänge, Z. Angew. Math. Mech., 3 (1923), 279–289.
P. Erdős, On the law of the iterated logarithm, Ann. of Math., 43 (1942), 419–436.
P. Erdős, On the integers having exactly k prime factors, Ann. of Math., 49 (1948), 53–66.
P. Erdős and M. Kac, On certain limit theorems of the theory of probability, Bull Amer. Math. Soc., 52 (1946), 292–302.
P. Erdős and M. Kac, On the number of positive sums of independent random variables, Bull. Amer. Math. Soc, 53 (1947), 1011–1020.
P. Erdős and A. Rényi, On random graphs I. Puhl Math. Debrecen, 6 (1959), 290–297.
P. Erdős and A. Rényi, Some further statistical properties of the digits in Cantor’s series, Acta Math. Acad. Sei. Hung., 10 (1959), 21–29.
P. Erdős and A. Rényi, On Cantor’s series with convergent Σ1/qn, Ann. Univ. Sei. Budapest. Eötvös Sect. Math., 2 (1959), 93–109.
P. Erdős and A. Rényi, On the strength of connectedness of a random graphs, Acta Math. Acad. Sei. Hung., 12 (1961), 262–267.
P. Erdős and A. Rényi, Some remarks on the large sieve of Yu. V. Linnik, Ann. Univ. Sei. Budapest. Eötvös Sect. Math., 11, (1968), 3–13.
P. Erdős and A. Rényi, On a new law of large numbers, J. Analyse Math., 23 (1970), 103–111.
P. Erdős, A. Rényi and P. Szüsz, On Engel’s and Sylvester’s series, Ann. Univ. Sei. Budapest. Eötvös Sect. Math., 1 (1958), 7–32.
P. Erdős and P. Révész, On the length of the longest head-run, in: Topics in Information Theory. Coll. Math. Soc. J. Bolyai, 16 (1976), 219–228 (ed. Imre Csiszár, P. Elias).
P. Erdős and P. Révész, On the favourite points of a random walk, Math. Structures Comput. Math. Modelling, 2 Sofia (1984), 152–157.
P. Erdős and P. Révész, Problems and results on random walks, Math. Stat, and Probab. Th., Proc. of the 6th Pannonian Symp. Vol. B (1986), 59–65.
P. Erdős and P. Révész, On the area of the circles covered by a random walk, J. of Multivariate Anal, 27 (1988), 169–180.
P. Erdős and P. Révész, Three problems on the random walk in ℤd, Studia Sei. Math. Hung., 26 (1991), 309–320.
P. Erdős and S. J. Taylor, Some problems concerning the structure of random walk paths, Acta Math. Acad. Sei. Hung., 11 (1960), 137–162.
P. Erdős and S. J. Taylor, Some intersection properties of random walk paths, Acta Math. Acad. Sei. Hung., 11 (1960), 231–248.
P. Erdős and S. J. Taylor, Some problems concerning the structure of random walk paths, Acta Math. Acad. Sei. Hung., 11 (1960), 137–162.
J. Galambos and A. Rényi, On quadratic inequalities in probability theory, Studia Sei. Math. Hung., 3 (1968), 351–358.
B. Gyires, Eigenwerte verallgemeinerter Toeplitzscher Matrizen, Publ. Math. Debrecen, 4 (1956), 171–179.
B. Gyires, Eine Verallgemeinerung des zentralen Grenzwertsatzes, Acta Math. Acad. Sei. Hung., 13 (1962), 69–80.
B. Gyires, On the uncertainty of matrix-valued predictions, Proc. Colloq. Inform. Theory, Debrecen 1967, pp. 253–268 (1968).
B. Gyires, The extreme linear predictions of the matrix-valued stationary stochastic processes, Mathematical statistics and probability theory Vol. B (Bad Tatzmannsdorf, 1986), pp. 113–124, Reidel, Dordrecht, 1987.
B, Gyires, Linear approximations in convex metric spaces and the application in the mixture theory of probability theory, World Scientific Publishing Co. Inc., River Edge, NJ, 1993.
Gy. Hajós and A. Rényi, Elementary proofs of some basic facts concerning order statistics, Acta Math. Acad. Sei. Hung., 5 (1954), 1–6.
L. Jánossy, A. Rényi and J. Aczél, On composed Poisson distributions, I. Acta Math. Acad. Sei. Hung., 1 (1950), 209–224.
J. Komlós, P. Major and G. Tusnády, An approximation of partial sums of independent R.V.’s and the sample D.F. I and IL, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 32 (1975), 111–131. and 34 (1976), 33–58.
J. Komlós and E. Szemerédy, Limit distributions for the existence of Hamilton cycles in a random graph, Discrete Math., 43 (1983), 55–63.
J. Komlós and G. Tusnády, On sequences of “pure heads”, Ann. Probab., 3 (1975), 608–617.
P. Lévy, Théorie de l’addition des variable aléatoires, Gauthier-Villars, Paris (1937).
P. Major, An improvement of Strassen’s invariance principle, Ann. Probab., 7 (1979), 55–61.
P. Medgyessy, Decomposition of superpositions of distribution functions, Akadémiai Kiadó, Budapest (1961).
J. Mogyoródi, Linear functionals on Hardy spaces, Ann. Univ. Sei. Budapest. Eötvös Sect. Math., 26 (1983), 161–174.
J. Mogyoródi, Maximal inequalities and Doob’s decomposition for non-negative supermartingales, Ann. Univ. Sei. Budapest Eötvös. Sect. Math., 26 (1983), 175–183.
T. F. Móri, Large deviation results for waiting times in repeated experiments, Acta Math. Acad. Sei. Hung., 45 (1985), 213–221.
T. F. Móri, Maximum waiting time when the size of the alphabet increases, Math. Statist, and Probab. Th. Proc. of the 6th Pannonian Symp. Vol. B (1986), 169–178.
G. Pólya, Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Strassennetz, Math. Ann., 84 (1921), 149–160.
G. Pólya, Zur Kinematik der Geschiebebewegung, Mitt. Versuchsinst. f. Wasserbau an der ETH, Zürich (1937), 1–21.
L. Pósa, Hamiltonian circuits in random graphs, Discrete Math., 14 (1976), 359–364.
A. Rényi, On the representation of an even number as the sum of a prime and of an almost prime, Izv. Akad. Nauk SSSR Ser. Mat, 12 (1948), 57–78.
A. Rényi, On the theory of order statistics, Acta Math. Acad. Sei. Hung., 4 (1953), 191–231.
A. Rényi, On a new axiomatic theory of probability, Acta Math. Acad. Sei. Hung., 6 (1955), 285–335.
A. Rényi, On the distribution of the digits in Cantor’s series, Mat. Lapok, 7 (1956), 77–100.
A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sei. Hung., 8 (1957), 477–493.
A. Rényi, Probabilistic methods in number theory, Shuxue Jinzhan, 4 (1958), 465–510.
A. Rényi, On Cantor’s products, Colloq. Math., 6 (1958), 135–139.
A. Rényi, On the probabilistic generalization of the large sieve of Linnik, MTA Mat. Kut. Int. Közl., 3 (1958), 199–206.
A. Rényi, New version of the probabilistic generalization of the large sieve, Acta Math. Acad. Sei. Hung., 10 (1959), 217–226.
A. Rényi, On measure of dependence, Acta Math. Acad. Sei. Hung., 10 (1959), 441–451.
A. Rényi, On the evaluation of random graphs, MTA Mat. Kut. Int. Közl, 5 (1960), 17–61.
A. Rényi, A general method for proving theorems in probability theory and some applications, MTA III. Oszt. Közl., 11 (1961), 79–105.
A. Rényi, A new approach to the theory of Engel’s series, Ann. Univ. Sei. Budapest. Eötvös Sect. Math., 5 (1962), 25–32.
A. Rényi, Remarks on the Poisson process, Studia Sei. Math. Hung., 2 (1967), 119–123.
A. Rényi and A. Prékopa, On the independence in the limit of sums depending on the same sequence of independent random variables, Acta Math. Acad. Sei. Hung., 7 (1956), 319–326.
A. Rényi and L. Takács, On processes generated by Poisson process and on their technical and physical applications, MTA Mat. Kut. Int. Közl., 1 (1952), 139–146.
P. Révész, Covering problems, Theory Probab. Appl., 38 (1993), 367–379.
V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 3 (1964), 211–226.
B. Tóth, No more than three favourite sites for simple random walk, Ann. Probab., 29 (2001), 484–503.
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Révész, P. (2006). Probability theory. In: Horváth, J. (eds) A Panorama of Hungarian Mathematics in the Twentieth Century I. Bolyai Society Mathematical Studies, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30721-1_15
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