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Branching processes, random trees, and a generalized scheme of arrangements of particles. (English) Zbl 0401.60082


MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory

Citations:

Zbl 0363.60070
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Full Text: DOI

References:

[1] B. A. Sevast’yanov, Branching Processes [in Russian], Nauka, Moscow (1971).
[2] O. V. Viskov, ”Some remarks on branching processes,” Mat. Zametki,8, No. 4, 409–418 (1970).
[3] M. Dwass, ”The total progeny in a branching process,” J. Appl. Prob.,6, No. 3, 682–686 (1969). · Zbl 0192.54401 · doi:10.2307/3212112
[4] V. F. Kolchin, B. A. Sevast’yanov, and V. P. Chistyakov, Random Arrangements [in Russian], Nauka, Moscow (1976).
[5] V. F. Kolchin, ”A class of limit theorems for conditional distributions,” Litov. Mat. Sb.,8, No. 1, 53–63 (1968). · Zbl 0235.60023
[6] D. P. Kennedy, ”The Galton-Watson process conditioned on the total progeny,” J. Appl. Prob.,12, No. 4, 800–806 (1975). · Zbl 0322.60072 · doi:10.2307/3212730
[7] V. E. Stepanov, ”On the distribution of the number of vertices in layers of a random tree,” Teor. Veroyatn. Ee Prim.,14, No. 1, 64–77 (1969). · Zbl 0172.21902
[8] A. Renyi, ”Some remarks on the theory of trees,” Publ. Math. Inst. Hung. Acad. Sci.,4, No. 7, 3–85 (1959).
[9] J. Moon, ”On nodes of degree two in random tree,” Mat.,15, No. 2, 188–192 (1968). · Zbl 0167.17205
[10] V. E. Stepanov, ”Random graphs, questions of cybernetics,” in: Transactions of the Seminar on Combinatorial Mathematics [in Russian], Moscow (1973), pp. 164–185.
[11] V. E. Stepanov, ”Limit distributions of some characteristics of random mappings,” Teor. Veroyatn. Ee Prim.,14, No. 4. 639–653 (1969). · Zbl 0204.51602
[12] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley (1968). · Zbl 0056.36001
[13] V. P. Chistyakov, ”Local limit theorems of the theory of random branching processes,” Teor. Veroyatn. Ee Prim.,2, No. 3, 360–374 (1957);10, No. 3, 597–598 (1965). · Zbl 0089.34301
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