Large deviations for Gibbs ensembles of the classical Toda chain*

被引：6

作者：

Guionnet, Alice ^{[1
]}

Memin, Ronan ^{[1
]}

机构：

[1] Univ Lyon, CNRS, ENSL, Lyon, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2022年 / 27卷

基金：

欧洲研究理事会;

关键词：

Toda chain; generalized Gibbs ensemble; random matrices; large deviations; beta;

D O I：

10.1214/22-EJP771

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove large deviation principles for the distribution of the empirical measure of the eigenvalues of Lax matrices following the Generalized Gibbs ensembles of the classical Toda chain introduced in [9]. We deduce the almost sure convergence of this empirical measure towards a limit which we describe in terms of the limiting empirical measure of Beta-ensembles. Our results apply to general smooth potentials.

引用

页数：30

共 11 条

[1]

[Anonymous], 2010, STOCHASTIC MODELLING

[2]

[Anonymous], 2010, CAMBRIDGE STUDIES AD

[3] Matrix models for beta ensembles [J].