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arXiv · 1812.06929

The one-dimensional log-gas free energy has a unique minimiser

Matthias Erbar·Martin Huesmann·Thomas Leblé
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Abstract

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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Matthias Erbar, Martin Huesmann, Thomas Leblé. 2018-12-17. The one-dimensional log-gas free energy has a unique minimiser. https://arxiv.org/abs/1812.06929

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