ON THE STATISTICAL-MECHANICS APPROACH IN THE RANDOM-MATRIX THEORY - INTEGRATED DENSITY-OF-STATES

被引：93

作者：

DEMONVEL, AB ^{[1
]}

PASTUR, L ^{[1
]}

SHCHERBINA, M ^{[1
]}

机构：

[1] KHARKOV LOW TEMP PHYS & ENGN INST,DIV MATH,KHARKOV 310164,UKRAINE

来源：

JOURNAL OF STATISTICAL PHYSICS | 1995年 / 79卷 / 3-4期

关键词：

RANDOM MATRIX; INTEGRATING DENSITY OF STATES; STATISTICAL MECHANICS; MEAN FIELD-THEORY;

D O I：

10.1007/BF02184872

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the ensemble of random symmetric n x n matrices specified by an orthogonal invariant probability distribution. We treat this distribution as a Gibbs measure of a mean-field-type model. This allows us to show that the normalized eigenvalue counting function of this ensemble converges in probability to a nonrandom limit as n --> infinity and that this limiting distribution is the solution of a certain self-consistent equation.

引用

页码：585 / 611

页数：27