Modified logarithmic Sobolev inequalities for canonical ensembles

Max Fathi

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arXiv · 1306.1484

Modified logarithmic Sobolev inequalities for canonical ensembles

Max Fathi

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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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BibTeX RIS

Max Fathi. 2014-06-19. Modified logarithmic Sobolev inequalities for canonical ensembles. https://arxiv.org/abs/1306.1484

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