Moderate Deviations for the Size of the Largest Component in a Super-critical Erdos-Renyi Graph

被引：0

作者：

Ameskamp, J. ^{[1
]}

Loewe, M. ^{[1
]}

机构：

[1] Univ Munster, Fachbereich Math, D-48149 Munster, Germany

来源：

MARKOV PROCESSES AND RELATED FIELDS | 2011年 / 17卷 / 03期

关键词：

moderate deviations; random graphs; large deviations; limit theorems;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the size of the largest component of a supercritical Erdos-Renyi graph g(n, p), in the regime where p = lambda/n and lambda > 1. It is well known that the largest component is of order zeta(lambda)n where zeta(lambda) is the extinction probability of a supercritical Calton-Watson process. We prove a Moderate Deviation Principle for the size of the largest component around this value, thus closing the gap between the Central Limit Theorem and a Large Deviation Principle.

引用

页码：369 / 390

页数：22

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