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Semicircle law for a matrix ensemble with dependent entries

2014/01/26 by Winfried Hochstättler, Werner Kirsch, Hochstättler, Winfried +3
Computer Science · Mathematics · #15B52 (Secondary) #60B20 (Primary) 60K35 #Bayesian Methods and Mixture Models #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1401.6636

openalex publication_date 2014/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the eigenvalue distribution measure. In case of Curie-Weiss distributions this criterion applies above the critical temperature (i.e. β<1). We also investigate the largest eigenvalue of certain ensembles of Curie-Weiss type and find a transition in its behavior at the critical temperature.

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