First order asymptotics of matrix integrals; A rigorous approach towards the understanding of matrix models

被引：32
|
作者：
Guionnet, A [1 ]
机构：
[1] Ecole Normale Super Lyon, Unite Math Pures & Appl, UMR 5669, F-69364 Lyon 07, France
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2004年 / 244卷 / 03期
关键词：
D O I：
10.1007/s00220-003-0992-4
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We investigate the large N limit of spectral measures of matrices which relate to the Gibbs measures of a number of statistical mechanical systems on random graphs. These include the Ising and Potts models on random graphs. For most of these models, we prove that the spectral measures converge almost surely and describe their limit via solutions to an Euler equation for isentropic flow with negative pressure p(rho)=-3(-1)pi(2)rho(3).
引用
收藏
页码：527 / 569
页数：43
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