Open Access
2016 Spectral Density for Random Matrices with Independent Skew-Diagonals
Kristina Schubert
Electron. Commun. Probab. 21: 1-12 (2016). DOI: 10.1214/16-ECP3


We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same skew-diagonal and we distinguish between two types of such correlations, a rather weak and a rather strong one. For weak correlations the limiting distribution is Wigner’s semi-circle distribution; for strong correlations it is the free convolution of the semi-circle distribution and the limiting distribution for random Hankel matrices.


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Kristina Schubert. "Spectral Density for Random Matrices with Independent Skew-Diagonals." Electron. Commun. Probab. 21 1 - 12, 2016.


Received: 9 February 2016; Accepted: 18 April 2016; Published: 2016
First available in Project Euclid: 12 May 2016

zbMATH: 1338.60015
MathSciNet: MR3510248
Digital Object Identifier: 10.1214/16-ECP3

Primary: 60B20 , 60F15 , 60K35

Keywords: dependent matrix entries , empirical eigenvalue distribution , semi-circle distribution

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