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2011 On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries
Radoslaw Adamczak
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Electron. J. Probab. 16: 1065-1095 (2011). DOI: 10.1214/EJP.v16-899

Abstract

In the first part of the article we prove limit theorems of Marchenko-Pastur type for the average spectral distribution of random matrices with dependent entries satisfying a weak law of large numbers, uniform bounds on moments and a martingale like condition investigated previously by Goetze and Tikhomirov. Examples include log-concave unconditional distributions on the space of matrices. In the second part we specialize to random matrices with independent isotropic unconditional log-concave rows for which (using the Tao-Vu replacement principle) we prove the circular law.

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Radoslaw Adamczak. "On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries." Electron. J. Probab. 16 1065 - 1095, 2011. https://doi.org/10.1214/EJP.v16-899

Information

Accepted: 2 June 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1221.15049
MathSciNet: MR2820070
Digital Object Identifier: 10.1214/EJP.v16-899

Subjects:
Primary: 15B52

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Vol.16 • 2011
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