On the Marchenko-Pastur and circular laws for some classes of random matrices with dependent entries

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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 Götze 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. © 2011 Applied Probability Trust.

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APA

Adamczak, R. (2011). On the Marchenko-Pastur and circular laws for some classes of random matrices with dependent entries. Electronic Journal of Probability, 16, 1065–1095. https://doi.org/10.1214/EJP.v16-899

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