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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


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.


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

Primary: 60B20
Secondary: 60F15 , 60K35

Keywords: Curie-Weiss model , Dependent random variables , random matrices , semicircle law , Toeplitz matrices

Vol.18 • 2013
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