English

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