On the maximal size of tree in a random forest

被引：0

作者：

Pavlov, Yuriy L. ^{[1
]}

机构：

[1] RAS, Inst Appl Math Res, Karelian Res Ctr, Petrozavodsk, Russia

来源：

DISCRETE MATHEMATICS AND APPLICATIONS | 2024年 / 34卷 / 04期

关键词：

Galton-Watson forest; tree size; vertex degree; limit theorems;

D O I：

10.1515/dma-2024-0019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Galton-Watson forests consisting of N rooted trees and n non-root vertices are considered. The distribution of the forest is determined by that of critical branching process with infinite variance and regularly varying tail of the progeny distribution. We prove limit theorem for the maximal size of a tree in a forest as N, n -> infinity in such a way that n/N -> infinity. Our conditions are significantly wider than was previously known.

引用

页码：221 / 232

页数：12

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