Instanton Approach to Large N Harish-Chandra-Itzykson-Zuber Integrals

被引：22

作者：

Bun, J. ^{[1
,2
,3
]}

Bouchaud, J. P. ^{[1
]}

Majumdar, S. N. ^{[2
]}

Potters, M. ^{[1
]}

机构：

[1] Capital Fund Management, F-75007 Paris, France

[2] Ctr Univ Orsay, CNRS, LPTMS, F-91405 Orsay, France

[3] Pole Univ Leonard de Vinci, DeVinci Finance Lab, F-92916 Paris, France

来源：

PHYSICAL REVIEW LETTERS | 2014年 / 113卷 / 07期

关键词：

ASYMPTOTICS; MATRIX;

D O I：

10.1103/PhysRevLett.113.070201

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We reconsider the large N asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

引用

页数：5

共 15 条

[1]

Bun J., IN PRESS

[2]

Collins B, 2003, INT MATH RES NOTICES, V2003, P953

[3] Asymptotics of unitary and orthogonal matrix integrals [J].