The missing log in large deviations for triangle counts

被引：41
|
作者：
Chatterjee, Sourav [1 ]
机构：
[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA
来源：
RANDOM STRUCTURES & ALGORITHMS | 2012年 / 40卷 / 04期
基金：
美国国家科学基金会;
关键词：
Erdos-Renyi random graph; tail bound; concentration inequalities; large deviations; SMALL SUBGRAPHS; RANDOM GRAPH; NUMBER; INEQUALITIES;
D O I：
10.1002/rsa.20381
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
This paper solves the problem of sharp large deviation estimates for the upper tail of the number of triangles in an Erdos-Renyi random graph, by establishing a logarithmic factor in the exponent that was missing till now. It is possible that the method of proof may extend to general subgraph counts. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 437451, 2012
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页码：437 / 451
页数：15
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