Non-Gaussian Limiting Laws for the Entries of Regular Functions of the Wigner Matrices

2011/03/11 by Anna Lytova, Lytova, A., L. А. Pastur +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1103.2345

openalex publication_date 2011/03/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper is a continuation of our paper "Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices", J. Stat. Phys. (134), 147--159 (2009), in which we proved the Central Limit Theorem for the matrix elements of differential functions of the real symmetric random Gaussian matrices (GOE). Here we consider the real symmetric random Wigner matrices having independent (modulo symmetry conditions) but not necessarily Gaussian entries. We show that in this case the matrix elements of sufficiently smooth functions of these random matrices have in general another limiting law which coincides essentially with the probability law of matrix entries.

Cited by

• The Common Limit of the Linear Statistics of Zeros of Random Polynomials and Their Derivatives

Related

• On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices
• Limiting spectral distribution for Wigner matrices with dependent entries
• Gaussian fluctuations of the determinant of Wigner Matrices
• Gaussian fluctuations for linear spectral statistics of deformed Wigner matrices
• CLT for spectra of submatrices of Wigner random matrices