Year: 2022
Type: article
Abstract: We consider the probability measure minimizing a free energy functional equal to the sum of a Coulomb interaction, a confinement potential and an entropy term, which arises in the statistical mechanics of Coulomb gases. In the limit where the inverse temperature β tends to ∞ the entropy term disappears and the measure, which we call the “thermal equilibrium measure” tends to the well-known equilibrium measure, which can also be interpreted as a solution to the classical obstacle problem. We provide quantitative estimates on the convergence of the thermal equilibrium measure to the equilibrium measure in strong norms in the bulk of the latter, with a sequence of explicit correction terms in powers of β - 1 , as well as an analysis of the tail after the boundary layer of size β - 1 / 2 .
DOI: 10.5802/afst.1714
Authors: Scott Armstrong, Sylvia Serfaty
Language: French
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
OpenAlex ID: W2997406370