Large deviations for spectral measures of some spiked matrices

被引：1

作者：

Noiry, Nathan ^{[1
]}

Rouault, Alain ^{[2
]}

机构：

[1] Telecom Paris, F-91120 Palaiseau, France

[2] Univ Paris Saclay, CNRS, UVSQ, Lab Math Versailles, F-78035 Versailles, France

来源：

RANDOM MATRICES-THEORY AND APPLICATIONS | 2022年 / 11卷 / 04期

关键词：

Large deviations; sum rules; Jacobi coefficients; Verblunsky coefficients; matrix measures; relative entropy; LARGEST EIGENVALUE; PHASE-TRANSITION; SUM-RULES; PERTURBATIONS; JACOBI;

D O I：

10.1142/S2010326322500393

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large deviations principle of unperturbed models derived in the previous work "Sum rules via large deviations" (Gamboa et al. [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509-559]).

引用

页数：35

共 43 条

[1]

ANDERSON G. W., 2010, Cambridge Studies in Advanced Mathematics, V118

[2]

[Anonymous], 2005, AMS Colloquium Series

[3] Bochner-Pearson-type characterization of the free Meixner class [J].