2017/11/28 by A. A. Ruzmaikina, Ruzmaikina, Anastasia A.
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1711.10438
openalex publication_date 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider Wigner random matrices -- symmetric n by n random matrices whose entries are independent identically distributed real random variables. We prove that the probability distribution of one or several eigenvalues close to the center of the spectrum does not depend on the probability distribution of the entries of the matrix and is the same as for the Gaussian Orthogonal Ensemble. We make only mild smoothness assumptions on the probability distribution of the entries and assume that the probability distribution of the entries decays polynomially with sufficiently large power or faster than polynomially.