The semicircle law for matrices with ergodic entries

被引：3

作者：

Loewe, Matthias ^{[1
]}

机构：

[1] Univ Munster, Fachbereich Math & Informat, Einsteinstr 62, D-48149 Munster, Germany

来源：

STATISTICS & PROBABILITY LETTERS | 2018年 / 141卷

关键词：

Random matrix; Semi-circle law; Dependent entries; Ergodicity; Decay of correlations; TOEPLITZ MATRICES; EIGENVALUES; ENSEMBLE;

D O I：

10.1016/j.spl.2018.05.025

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 study the empirical spectral distribution (ESD) of symmetric random matrices with ergodic entries on the diagonals. We observe that for entries with correlations that decay to 0, when the distance of the diagonal entries becomes large the limiting ESD is the well known semicircle law. If it does not decay to 0 (and have the same sign) the semicircle law cannot be the limit of the ESD. This is in good agreement with results on exchangeable processes analyzed in Friesen and Lowe (2013) and Hochstattler et al. (2016). (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：90 / 95

页数：6

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