On the largest component of a random graph with a subpower-law degree sequence in a subcritical phase

被引：5

作者：

Pittel, B. G. ^{[1
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2008年 / 18卷 / 04期

基金：

美国国家科学基金会;

关键词：

random graph; degree sequence; power law; largest cluster; pairing process; martingale; asymptotic; bounds;

D O I：

10.1214/07-AAP493

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：

A uniformly random graph on n vertices with a fixed degree sequence, obeying a y subpower law, is studied. It is shown that, for y > 3, in a subcritical phase with high probability the largest component size does not exceed n I /Y +E,, -n = 0 (In In n1 In n), I ly being the best power for this random graph. This is similar to the best possible n'l(y-') bound for a different model of the random graph, one with independent vertex degrees, conjectured by Durrett, and proved recently by Janson.

引用

页码：1636 / 1650

页数：15

共 9 条

[1]

[Anonymous], 2011, Random Graphs

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