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.
"Spectral Density for Random Matrices with Independent Skew-Diagonals." Electron. Commun. Probab. 21 1 - 12, 2016. https://doi.org/10.1214/16-ECP3