Large Deviation Principle for local empirical measure of Coulomb gases at intermediate temperature regime

Abstract

This paper deals 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. In the critical temperature scaling regime, we derive an LDP-type result in which the "rate function" features the competition of an entropy and energy terms. An important idea in this work is to exploit the different scaling relations satisfied by the Coulomb energy and the entropy.

arXiv commentFilled gap in proof

References in corpus (7)

• Asymptotic expansion of beta matrix models in the one-cut regime
• Edge Universality of Beta Ensembles
• Mean Field Limit for Coulomb-Type Flows
• First order global asymptotics for confined particles with singular pair repulsion
• Fluctuations of linear eigenvalue statistics of $\beta$ matrix models in the multi-cut regime
• Concentration for Coulomb gases and Coulomb transport inequalities
• Concentration for Coulomb gases on compact manifolds

Cited by in corpus (1)

• Dynamical large deviations for plasmas below the Debye length and the Landau equation