Martin Venker (University of Bielefeld) : Edge Statistics of Particle Systems with Repulsive Interaction

Thursday 17 Mar 2016, 16:15 → 17:30 Europe/Brussels

CYCL05 (Marc de Hemptinne)

Abstract: We will consider a class of interacting particle systems on the real line which generalizes eigenvalue ensembles of Hermitian random matrices by allowing different interactions between particles. We will show how these models can be represented as averages of determinantal ensembles. An extensive description of the distributional properties of the largest particle will be provided, including the (strong) law of large numbers, a fluctuation limit theorem and fine asymptotics of the upper tail deviations. In particular, our results describe the transition between universal behavior in the regime of the Tracy-Widom law and non-universal behavior for large deviations of the rightmost particle. In addition, we show that the limiting correlations of particles close to the edge are given in terms of the Airy kernel. This talk is based on joint work with Thomas Kriecherbauer.