Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI:10.1515/dma-2023-0019

Elena V. Khvorostianskaia

引用次数: 0

Abstract

Abstract We consider a critical Galton – Watson branching process starting with N particles; the number of offsprings is supposed to have the distribution pk=(k + 1)−τ−(k + 2)−τ, k=0, 1, 2, … Limit distributions of the maximal tree size are obtained for the corresponding Galton – Watson forest with N trees and n non-root vertices as N, n → ∞, n/Nτ ⩾ C > 0.

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Galton最大树大小的极限定理 – 危急情况下的Watson森林

摘要我们认为一个关键的Galton – 从N粒子开始的Watson分支过程；子代的数量应该具有分布pk＝（k + 1） -τ−（k + 2） -τ，k=0，1，2，…得到了相应Galton的最大树大小的极限分布 – 具有N棵树和N个非根顶点为N，N的Watson森林 → ∞, n/nτ⩾C > 0

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.