Spectral density for random matrices with independent skew-diagonals. (English) Zbl 1338.60015

Schubert, Kristina

Electron. Commun. Probab. 21, Paper No. 40, 12 p. (2016).

Summary: 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.

MSC:

60B20	Random matrices (probabilistic aspects)
15B52	Random matrices (algebraic aspects)
60F15	Strong limit theorems
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

empirical eigenvalue distribution; dependent matrix entries; semi-circle distribution