Modified logarithmic Sobolev inequalities for canonical ensembles

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 $W_p$ for Kawasaki dynamics on the Ginzburg-Landau model.

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