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Pré-Publication, Document De Travail Année : 2020

Local microscopic behavior for 2D Coulomb gases

Thomas Leblé

Résumé

The study of two-dimensional Coulomb gases lies at the interface of statistical physics and non-Hermitian random matrix theory. In this paper we give a large deviation principle (LDP) for the empirical fields obtained, under the canonical Gibbs measure, by zooming around a point in the bulk of the equilibrium measure, up to the finest averaging scale N −1/2+ε. The rate function is given by the sum of the "renormalized energy" of Serfaty et al. weighted by the inverse temperature, and of the specific relative entropy. We deduce a local law which quantifies the convergence of the empirical measures of the particles to the equilibrium measure, up to the finest scale.
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hal-03040308 , version 1 (04-12-2020)

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  • HAL Id : hal-03040308 , version 1

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Thomas Leblé. Local microscopic behavior for 2D Coulomb gases. 2020. ⟨hal-03040308⟩
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