1996/06/24 by A. Khorunzhy, Alexei M. Khorunzhy, Boris A. Khoruzhenko +2 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Random Matrices and Applications #Stochastic processes and statistical mechanics #cond-mat
paper · pdf · doi:10.1063/1.531589
29 pages, LaTeX (revtex style files required) submitted to Journ Math Phys
arxiv created 1996/06/24 · openalex publication_date 1996/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the normalized trace gn(z)=n−1 tr(H−zI)−1 of the resolvent of n×n real symmetric matrices H=[(1+δjk)Wjk√n]j,k=1n assuming that their entries are independent but not necessarily identically distributed random variables. We develop a rigorous method of asymptotic analysis of moments of gn(z) for | Iz|≥η0 where η0 is determined by the second moment of Wjk. By using this method we find the asymptotic form of the expectation Egn(z) and of the connected correlator Egn(z1)gn(z2)−Egn(z1)Egn (z2). We also prove that the centralized trace ngn(z)−Engn(z) has the Gaussian distribution in the limit n=∞. Based on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles.