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2013 A phase transition for the limiting spectral density of random matrices
Olga Friesen, Matthias Löwe
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Electron. J. Probab. 18: 1-17 (2013). DOI: 10.1214/EJP.v18-2118

Abstract

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated. Depending on the strength of correlation, the limiting spectral distribution is either the famous semicircle distribution, the distribution derived for Toeplitz matrices by Bryc, Dembo and Jiang (2006), or the free convolution of the two distributions.

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Olga Friesen. Matthias Löwe. "A phase transition for the limiting spectral density of random matrices." Electron. J. Probab. 18 1 - 17, 2013. https://doi.org/10.1214/EJP.v18-2118

Information

Accepted: 29 January 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1287.60011
MathSciNet: MR3035745
Digital Object Identifier: 10.1214/EJP.v18-2118

Subjects:
Primary: 60B20
Secondary: 60F15, 60K35

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