Student Probability Seminar

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Large Deviations Principles for Coulomb Gases

Speaker: Luke Peilen, CIMS

Location: Warren Weaver Hall 201

Date: Thursday, November 14, 2019, 12:15 p.m.

Synopsis:

This expository talk will focus on the large deviations properties of Coulomb gases, a class of particle systems with singular interaction energies important to statistical mechanics and random matrix theory. I will first discuss various classical results on minimizers and their asymptotics, before discussing two large deviations principles. The first, based on the work of Petz and Hiai in the late nineties, describes the macroscopic behavior of the points and shows that in the small temperature regime this behavior is independent of the temperature. The second, due to Leblé and Serfaty, describes the asymptotic behavior at the level of point processes and obtains a more refined asymptotic expansion of the partition function.