David Padilla-Garza : Large Deviation Principle for local empirical measure of Coulomb gases at intermediate temperature regime

Posted by Ian Tobasco , part of the Analysis and Applied Mathematics Seminar.

At

April 5, 2021, 4 p.m.

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Abstract

We work with Coulomb gases at an intermediate temperature regime. We define a local empirical field and identify a critical temperature scaling. We show that if the scaling of the temperature is supercritical, the local empirical field satisfies an LDP with an entropy-based rate function. We also show that if the scaling of the temperature is subcritical, the local empirical field satisfies an LDP with an energy-based rate function. An important idea in this work is to exploit the different scaling relations satisfied by the Coulomb energy and the entropy.