Kristina Schubert (University of Muenster) : Wigner's semi-circle law for random matrices with dependent entries

Thursday 6 Apr 2017, 15:00 → 17:00 Europe/Brussels

CYCL09B (MdeHemptinne)

Abstract: Wigner's semi-circle law states that the spectral distribution of random matrices with independent entries converges to the semi-circle distribution. Since its original version, proved by Wigner in the 1950s, there have been a number of generalization of this statement for various random matrix ensembles. We review some more recent results about the validity of this law for matrices with dependent entries. In particular, we consider matrices, where the matrix entries are given by a stochastic process with decaying correlations. In this case, the way we fill the stochastic process into the matrix, determines whether the limiting spectral distribution is the semi-circle or not.