Resolvent of Large Random Graphs

被引：71

作者：

Bordenave, Charles ^{[1
,2
]}

Lelarge, Marc ^{[3
]}

机构：

[1] Univ Toulouse, Inst Math, Toulouse, France

[2] CNRS, F-75700 Paris, France

[3] Ecole Normale Super, INRIA, Projet TREC, F-75231 Paris, France

来源：

RANDOM STRUCTURES & ALGORITHMS | 2010年 / 37卷 / 03期

关键词：

random graphs; spectral measure; local convergence; Galton-Watson tree; EIGENVALUE DISTRIBUTION; MATRICES; SPECTRUM; STATES; LIMITS;

D O I：

10.1002/rsa.20313

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and derive a new formula for the Stieltjes transform of the spectral measure of such graphs. We illustrate our results on the uniform regular graphs, Erdos-Renyi graphs and graphs with a given degree sequence. We give examples of application for weighted graphs, bipartite graphs and the uniform spanning tree of n vertices. 2010 Wiley Periodicals, Inc. Random Struct. Alg., 37, 332-352, 2010

引用

页码：332 / 352

页数：21

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