Semicircle Law for a Matrix Ensemble with Dependent Entries

Winfried Hochstättler (), Werner Kirsch () and Simone Warzel ()
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Winfried Hochstättler: FernUniversität in Hagen
Werner Kirsch: FernUniversität in Hagen
Simone Warzel: Technische Universität München

Journal of Theoretical Probability, 2016, vol. 29, issue 3, 1047-1068

Abstract: 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., $$\beta \,

Keywords: Random matrices; Semicircle law; Curie–Weiss model; 60B20; 05C45; 60K35; 82B20 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10959-015-0602-3

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