Electronic Communications in Probability

Spectral Density for Random Matrices with Independent Skew-Diagonals

Kristina Schubert

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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.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 40, 12 pp.

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

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Zentralblatt MATH identifier

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 60F15: Strong theorems 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

empirical eigenvalue distribution dependent matrix entries semi-circle distribution

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Schubert, Kristina. Spectral Density for Random Matrices with Independent Skew-Diagonals. Electron. Commun. Probab. 21 (2016), paper no. 40, 12 pp. doi:10.1214/16-ECP3. https://projecteuclid.org/euclid.ecp/1463081069

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