Large Deviations Principles for Coulomb gases at intermediate temperature regime
In this talk, we will begin by reviewing the notion of LDP, and some well-known LDPs in many-particle systems. We will then specialize in Coulomb gases at an intermediate temperature regime. We define a local empirical field and identify a critical temperature scaling. We show that if the temperature scaling is supercritical, the local empirical field satisfies an LDP with an entropy-based rate function. We also show that if the temperature scaling is subcritical, the local empirical field satisfies an LDP with an energy-based rate function. In the critical temperature scaling regime, we derive an LDP-type result in which the "rate function" features the competition of entropy and energy terms.