Spectral Density for Random Matrices with Independent Skew-Diagonals

Kristina Schubert

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arXiv · 1510.06448

Spectral Density for Random Matrices with Independent Skew-Diagonals

Kristina Schubert

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Abstract

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. 2015-10-21. Spectral Density for Random Matrices with Independent Skew-Diagonals. https://arxiv.org/abs/1510.06448

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