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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1977, Volume 21, Issue 5, Pages 691–705 (Mi mz8000)

Branching processes, random trees, and a generalized scheme of arrangements of particles

V. F. Kolchin

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: It is shown that the conditional distributions of a number of characteristics of a branching process $\mu(t)$, $\mu(0)=m$, under the condition that the number of total progeny $\nu_m$ 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 $\mu(t)$, $\mu(0)=1$, under the condition that $\nu_1=n+1$, coincide with the characteristics of a random tree. By using these connections we obtain in this article a series of limit theorems as $n\to\infty$ for characteristics of random trees and branching processes under the conditions that $\nu_m=n$.

Full text: PDF file (1084 kB)

English version:
Mathematical Notes, 1977, 21:5, 386–394

Bibliographic databases:

UDC: 519.1

Citation: V. F. Kolchin, “Branching processes, random trees, and a generalized scheme of arrangements of particles”, Mat. Zametki, 21:5 (1977), 691–705; Math. Notes, 21:5 (1977), 386–394

Citation in format AMSBIB
\Bibitem{Kol77} \by V.~F.~Kolchin \paper Branching processes, random trees, and a~generalized scheme of arrangements of particles \jour Mat. Zametki \yr 1977 \vol 21 \issue 5 \pages 691--705 \mathnet{http://mi.mathnet.ru/mz8000} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=458613} \zmath{https://zbmath.org/?q=an:0401.60082|0363.60070} \transl \jour Math. Notes \yr 1977 \vol 21 \issue 5 \pages 386--394 \crossref{https://doi.org/10.1007/BF01788236}