Student Probability Seminar
Large Deviations Principles for Coulomb Gases
Speaker: Luke Peilen, CIMS
Date: Wednesday, November 18, 2020, 10 a.m.
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 start by discussing two large deviations principles, whose arguments illustrate some of the difficulties and techniques at play. 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 demonstrates how in a different scaling we start to see the effects of temperature. Time permitting, I will also discuss more recent results of Leblé-Serfaty and Armstrong-Serfaty concerning more refined large deviations principles.