The one-dimensional log-gas free energy has a unique minimiser
Probability
2018-12-18 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1812.06929,
title = {The one-dimensional log-gas free energy has a unique minimiser},
author = {Matthias Erbar and Martin Huesmann and Thomas Leblé},
journal= {arXiv preprint arXiv:1812.06929},
year = {2018}
}
Comments
45 pages