Poisson Statistics for Matrix Ensembles at Large Temperature

In this article, we consider -ensembles, i.e. collections of particles with random positions on the real line having joint distribution 1/Z(N)(beta) vertical bar Delta(lambda)vertical bar(beta) e(-N beta/4) Sigma(N)(i=1) lambda(2)(i) d lambda, in the regime where as . We briefly describe the global regime and then consider the local regime. In the case where stays bounded, we prove that the local eigenvalue statistics, in the vicinity of any real number, are asymptotically to those of a Poisson point process. In the case where , we prove a partial result in this direction.