Student Probability Seminar
Large Deviation Principle for local empirical measure of Coulomb gases at intermediate temperature regime
Speaker: David Padilla-Garza, TU Dresden
Date: Wednesday, March 17, 2021, 9 a.m.
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.