Localization and delocalization of eigenvectors for heavy-tailed random matrices

被引：43

作者：

Bordenave, Charles ^{[1
,2
]}

Guionnet, Alice ^{[3
,4
]}

机构：

[1] CNRS, F-31062 Toulouse, France

[2] Univ Toulouse, Inst Math Toulouse, F-31062 Toulouse, France

[3] CNRS, F-69364 Lyon 07, France

[4] Ecole Normale Super Lyon, Unite Math Pures & Appl, F-69364 Lyon 07, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2013年 / 157卷 / 3-4期

关键词：

Random matrices; Stable distribution; Eigenvector delocalization; Wegner estimate; SEMICIRCLE LAW; UNIVERSALITY; SPECTRUM; STATISTICS;

D O I：

10.1007/s00440-012-0473-9

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：

Consider an Hermitian random matrix with, above the diagonal, independent entries with -stable symmetric distribution and . We establish new bounds on the rate of convergence of the empirical spectral distribution of this random matrix as goes to infinity. When and , we give vanishing bounds on the -norm of the eigenvectors normalized to have unit -norm. On the contrary, when , we prove that these eigenvectors are localized.

引用

页码：885 / 953

页数：69

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