Branching processes,random trees,and a generalized scheme of arrangements of particles |
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Authors: | V F Kolchin |
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Institution: | (1) V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR |
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Abstract: | It is shown that the conditional distributions of a number of characteristics of a branching process (t), (0)=m, under the condition that the number of total progeny m in this process is equal to n, coincide with the distributions of the corresponding characteristics of a generalized scheme of arrangement of particles in cells. In the case where the number of offsprings of a particle has the Poisson distribution, the characteristics of the branching process (t), (0)=1, under the condition that 1=n+1, coincide with the characteristics of a random tree. By using these connections we obtain in this article a series of limit theorems as n for characteristics of random trees and branching processes under the conditions that m=n.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 691–705, May, 1977. |
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