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Book Review

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MathSciNet review: 1567712
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Valentin F. Kolchin
Title: Random mappings
Additional book information: Optimization Software, Inc., distributed by Springer-Verlag, New York, 1986, xiv+206 pp., $ 80.00. ISBN 0-387-96154-2.

References [Enhancements On Off] (What's this?)

  • 1. A. Cayley, A theorem on trees, Quart. J. Pure Appl. Math. 23 (1889), 376-378. [The Collected Mathematical Papers of Arthur Cayley, Vol. XIII, Cambridge Univ. Press, 1897, pp. 26-28.]
  • 2. Paul Erdős and Joel Spencer, Probabilistic methods in combinatorics, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Probability and Mathematical Statistics, Vol. 17. MR 0382007
  • 3. P. Erdős and P. Turán, On some problems of a statistical group-theory. III, Acta Math. Acad. Sci. Hungar. 18 (1967), 309–320. MR 215908, https://doi.org/10.1007/BF02280290
  • 4. B. V. Gnedenko, On a local limit theorem of the theory of probability, Uspehi Matem. Nauk (N. S.) 3 (1948), no. 3(25), 187–194 (Russian). MR 0026275
  • 5. S. W. Golomb, Random permutations, Bull. Amer. Math. Soc. 70 (1964), 747.
  • 6. W. Gontcharoff, Sur la distribution des cycles dans les permutations, C. R. (Doklady) Acad. Sci. URSS (N.S.) 35 (1942), 267–269. MR 0007207
  • 7. David G. Kendall, Some problems in the theory of queues, J. Roy. Statist. Soc. Ser. B 13 (1951), 151–173; discussion: 173–185. MR 47944
  • 8. V. F. Kolčin, A certain class of limit theorems for conditional distributions, Litovsk. Mat. Sb. 8 (1968), 53–63 (Russian, with Lithuanian and English summaries). MR 0240856
  • 9. V. F. Kolchin, A problem of the allocation of particles in cells and cycles of random permutations, Theor. Probability Appl. 16 (1971), 74-90.
  • 10. V. F. Kolčin, The extinction time of a branching process and the height of a random tree, Mat. Zametki 24 (1978), no. 6, 859–870, 894 (Russian). MR 522419
  • 11. Valentin F. Kolchin, Boris A. Sevast′yanov, and Vladimir P. Chistyakov, Random allocations, V. H. Winston & Sons, Washington, D.C.; distributed by Halsted Press [John Wiley & Sons], New York-Toronto, Ont.-London, 1978. Translated from the Russian; Translation edited by A. V. Balakrishnan; Scripta Series in Mathematics. MR 0471016
  • 12. Richard Otter, The multiplicative process, Ann. Math. Statistics 20 (1949), 206–224. MR 30716, https://doi.org/10.1214/aoms/1177730031
  • 13. Yu. L. Pavlov, The asymptotic distribution of maximum tree size in a random forest, Theor. Probability Appl. 22 (1977), 509-520.
  • 14. Yu. L. Pavlov, Limit distributions of the height of a random forest, Teor. Veroyatnost. i Primenen. 28 (1983), no. 3, 449–457 (Russian, with English summary). MR 716303
  • 15. G. V. Proskurin, The distribution of the number of vertices in the strata of a random mapping, Teor. Verojatnost. i Primenen. 18 (1973), 846–852 (Russian, with English summary). MR 0323608
  • 16. H. Prüfer, Neuer Beweis eines Satzes über Permutationen, Arch. Math. u. Phys. 27 (1918), 142-144.
  • 17. A. Rényi and G. Szekeres, On the height of trees, J. Austral. Math. Soc. 7 (1967), 497–507. MR 0219440
  • 18. V. N. Sačkov, Veroyatnostnye metody v kombinatornom analize, “Nauka”, Moscow, 1978 (Russian). MR 522165
  • 19. B. A. Sevastyanov and V. P. Chistyakov, Asymptotic normality in the classical ball problem, Theor. Probability Appl. 9 (1964), 198-211.
  • 20. L. A. Shepp and S. P. Lloyd, Ordered cycle lengths in a random permutation, Trans. Amer. Math. Soc. 121 (1966), 340–357. MR 195117, https://doi.org/10.1090/S0002-9947-1966-0195117-8
  • 21. Lajos Takács, Remarks on random walk problems, Magyar Tud. Akad. Mat. Kutató Int. Közl. 2 (1957), 3/4, 175–182 (English, with Hungarian and Russian summaries). MR 0102135
  • 22. Lajos Takács, A generalization of the ballot problem and its application in the theory of queues, J. Amer. Statist. Assoc. 57 (1962), 327–337. MR 138139
  • 23. Lajos Takács, Combinatorial methods in the theory of stochastic processes, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0217858

Review Information:

Reviewer: Lajos Takács
Journal: Bull. Amer. Math. Soc. 19 (1988), 511-515
DOI: https://doi.org/10.1090/S0273-0979-1988-15723-0