Volume 19, 2015
|Page(s)||544 - 559|
|Published online||01 December 2015|
Modified logarithmic Sobolev inequalities for canonical ensembles
LPMA, University Paris 6, France.
Revised: 19 June 2014
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 Wp for Kawasaki dynamics on the Ginzburg−Landau’s model.
Mathematics Subject Classification: 60K35 / 82B21
Key words: Modified logarithmic Sobolev inequalities / spin system / coarse-graining
© EDP Sciences, SMAI 2015
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