The Mixing Time of the Giant Component of a Random Graph

被引：36

作者：

Benjamini, Itai ^{[1
]}

Kozma, Gady ^{[1
]}

Wormald, Nicholas ^{[2
]}

机构：

[1] Weizmann Inst Sci, Dept Math, IL-76100 Rehovot, Israel

[2] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

来源：

RANDOM STRUCTURES & ALGORITHMS | 2014年 / 45卷 / 03期

基金：

以色列科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

mixing time; random walk; random graph; expander; giant component; INCIPIENT INFINITE CLUSTER; SIMPLE RANDOM-WALK; PERCOLATION; DIAMETER;

D O I：

10.1002/rsa.20539

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We show that the total variation mixing time of the simple random walk on the giant component of supercritical G(n,p) and G(n,m) is Theta(log(2) n). This statement was proved, independently, by Fountoulakis and Reed. Our proof follows from a structure result for these graphs which is interesting in its own right. We show that these graphs are "decorated expanders" - an expander glued to graphs whose size has constant expectation and exponential tail, and such that each vertex in the expander is glued to no more than a constant number of decorations. (C) 2014 Wiley Periodicals, Inc.

引用

页码：383 / 407

页数：25

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