THE ONE-DIMENSIONAL LOG-GAS FREE ENERGY HAS A UNIQUE MINIMISER - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2020

THE ONE-DIMENSIONAL LOG-GAS FREE ENERGY HAS A UNIQUE MINIMISER

Résumé

We prove that, at every positive temperature, the infinite-volume free energy of the one dimensional log-gas, or beta-ensemble, has a unique minimiser, which is the Sine-beta process arising from random matrix theory. We rely on a quantitative displacement convexity argument at the level of point processes, and on the screening procedure introduced by Sandier-Serfaty.
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Dates et versions

hal-03040306 , version 1 (04-12-2020)

Identifiants

  • HAL Id : hal-03040306 , version 1

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Matthias Erbar, Martin Huesmann, Thomas Leblé. THE ONE-DIMENSIONAL LOG-GAS FREE ENERGY HAS A UNIQUE MINIMISER. 2020. ⟨hal-03040306⟩

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