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Local statistics of particle systems with repulsive interaction

Banff International Research Station for Mathematical Innovation and Discovery

We consider interacting particle systems on the real line which generalize beta-ensembles by allowing for different pair interactions. We show how these models can be represented as averages of beta-ensembles with random external fields. Particular emphasis is put on models resembling the beta=2-ensembles where we present detailed asymptotics in the bulk and at the edge. In the bulk, these asymptotics allow to consider empirical spacings of unfolded particles. At the edge, we describe the gradual transition from universal behavior in the regime of the Tracy-Widom law to non-universal behavior for large deviations of the largest particle.

Mathematics; Probability theory and stochastic processes; Statistical mechanics, structure of matter

video/mp4

Author affiliation: Bielefeld University

2017-02-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59438

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/