Martin Venker (Bielefeld University), Local Statistics of Repulsive Particle Systems

Abstract: We will consider particle systems on the real line with pairwise interaction mimicking the repulsion between random eigenvalues. We show that the universal random matrix distributions also appear in this new class of models. Fine asymptotics will be given for a number of local statistics, including bulk and edge correlations, the distribution of the largest particle and the nearest-neighbor spacing distribution.