Fluctuations of linear statistics of half-heavy-tailed random matrices

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Benaych-Georges, Florent¹  Maltsev, Anna² 

[1] Univ Paris 05, MAP5, 45 Rue St Peres, F-75270 Paris 06, France

[2] Univ Bristol, Dept Math, Howard House, Bristol BS8 1SN, Avon, England

关键词: Random matrices;    Heavy tailed random variables;    Central limit theorem;   

DOI  :  10.1016/j.spa.2016.04.030

来源: Elsevier

【 摘 要 】

In this paper, we consider a Wigner matrix A with entries whose cumulative distribution decays as x(-alpha) with 2 < alpha < 4 for large x. We are interested in the fluctuations of the linear statistics N-1 Tr phi(A), for some nice test functions phi. The behavior of such fluctuations has been understood for both heavy-tailed matrices (i.e. alpha < 2) in Benaych-Georges (2014) and light-tailed matrices (i.e. alpha > 4) in Bai and Silverstein (2009). This paper fills in the gap of understanding it for 2 < alpha < 4. We find that while linear spectral statistics for heavy-tailed matrices have fluctuations of order N-1/2 and those for light-tailed matrices have fluctuations of order N-1, the linear spectral statistics for half-heavy-tailed matrices exhibit an intermediate alpha-dependent order of N (-alpha/4). (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free