Book Review
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MathSciNet review:
1567712
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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.
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.]
Paul Erdős and Joel Spencer, Probabilistic methods in combinatorics, Probability and Mathematical Statistics, Vol. 17, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0382007
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, DOI 10.1007/BF02280290
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.
W. Gontcharoff, Sur la distribution des cycles dans les permutations, C. R. (Doklady) Acad. Sci. URSS (N.S.) 35 (1942), 267–269. MR 0007207
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
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.
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
V. F. Kolchin, B. A. Sevast′yanov, and V. P. Chistyakov, Sluchaĭ nye razmeshcheniya, Teoriya Veroyatnosteĭ i Matematicheskaya Statistika. [Probability Theory and Mathematical Statistics], Izdat. “Nauka”, Moscow, 1976 (Russian). MR 0471015
Richard Otter, The multiplicative process, Ann. Math. Statistics 20 (1949), 206–224. MR 30716, DOI 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.
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
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.
A. Rényi and G. Szekeres, On the height of trees, J. Austral. Math. Soc. 7 (1967), 497–507. MR 0219440
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.
L. A. Shepp and S. P. Lloyd, Ordered cycle lengths in a random permutation, Trans. Amer. Math. Soc. 121 (1966), 340–357. MR 195117, DOI 10.1090/S0002-9947-1966-0195117-8
Lajos Takács, Remarks on random walk problems, Magyar Tud. Akad. Mat. Kutató Int. Közl. 2 (1957), 3/4, 175–182 (English, with Russian and Hungarian summaries). MR 102135
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
Lajos Takács, Combinatorial methods in the theory of stochastic processes, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0217858
- 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.
- P. Erdős and J. Spencer, Probabilistic methods in combinatorics, Akadémiai Kiadó, Budapest, 1974. 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
- 4.
- B. V. Gnedenko, On a local limit theorem in probability theory, Uspekhi Mat. Nauk 3, no. 3 (1948), 187-194. (Russian) MR 26275
- 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 35 (1942), 267-269. MR 7207
- 7.
- D. G. Kendall, Some problems in the theory of queues, J. Roy. Stat. Soc. Ser. B 13 (1951), 151-185. MR 47944
- 8.
- V. F. Kolchin, A certain class of limit theorems for conditional distributions, Litovsk. Mat. Sb. 8 (1968), 53-63. [English translation: Selected Translations in Mathematical Statistics and Probability 11 (1973), 185-197.] (Russian) MR 240856
- 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. Kolchin, Moment of degeneration of branching processes and height of a random tree, Math. Notes 24 (1978), 954-961. MR 522419
- 11.
- V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov, Random allocations, V. H. Winston and Sons, Washington, D.C., 1978. MR 471016
- 12.
- R. Otter, The multiplicative process, Ann. Math. Statist. 20 (1949), 206-224. MR 30716
- 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, Theor. Probability Appl. 28 (1984), 471-480. MR 716303
- 15.
- G. V. Proskurin, On the distribution of the number of vertices in strata of a random mapping, Theor. Probability Appl. 18 (1973), 803-808. MR 323608
- 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 219440
- 18.
- V. N. Sachkov, Probability methods in combinatorial analysis, "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 P. S. Lloyd, Ordered cycle length in a random permutation, Trans. Amer. Math. Soc. 121 (1966), 340-357. MR 195117
- 21.
- L. Takács, Remarks on random walk problems, Publ. Math. Inst. Hungar. Acad. Sci. 2 (1957), 175-182. MR 102135
- 22.
- L. 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.
- L. Takács, Combinatorial methods in the theory of stochastic processes, John Wiley and Sons, New York, 1967. MR 217858
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
