The Semicircle Law for Matrices with Independent Diagonals

Olga Friesen () and Matthias Löwe ()
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Olga Friesen: Westfälische Wilhelms-Universität Münster
Matthias Löwe: Westfälische Wilhelms-Universität Münster

Journal of Theoretical Probability, 2013, vol. 26, issue 4, 1084-1096

Abstract: Abstract We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real-valued entries and stochastically independent diagonals. Along the diagonals the entries may be correlated. We show that under sufficiently nice moment conditions the empirical eigenvalue distribution converges almost surely weakly to the semi-circle law.

Keywords: Random matrix; Semi-circle law; Dependent entries; 60K35 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-011-0383-2

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