English

Modified logarithmic Sobolev inequalities for canonical ensembles

Probability 2014-06-20 v2 Mathematical Physics math.MP

Abstract

In this paper, we prove modified logarithmic Sobolev inequalities for canonical ensembles with superquadratic single-site potential. These inequalities were introduced by Bobkov and Ledoux, and are closely related to concentration of measure and transport-entropy inequalities. Our method is an adaptation of the iterated two-scale approach that was developed by Menz and Otto to prove the usual logarithmic Sobolev inequality in this context. As a consequence, we obtain convergence in Wasserstein distance WpW_p for Kawasaki dynamics on the Ginzburg-Landau model.

Keywords

Cite

@article{arxiv.1306.1484,
  title  = {Modified logarithmic Sobolev inequalities for canonical ensembles},
  author = {Max Fathi},
  journal= {arXiv preprint arXiv:1306.1484},
  year   = {2014}
}

Comments

19 pages v2: a mistake has been corrected in the proof of Lemma 2.3 (formerly Lemma 2.8), and the presentation has been reworked

R2 v1 2026-06-22T00:29:20.504Z