Modified logarithmic Sobolev inequalities for canonical ensembles

2013/06/06 by Max Fathi, Fathi, Max
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1306.1484

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

arxiv created 2014/06/19 · arxiv updated 2014/06/20

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.

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