| Issue |
ESAIM: PS
Volume 19, 2015
|
|
|---|---|---|
| Page(s) | 544 - 559 | |
| DOI | https://doi.org/10.1051/ps/2015004 | |
| Published online | 01 December 2015 | |
Modified logarithmic Sobolev inequalities for canonical ensembles
LPMA, University Paris 6, France.
max.fathi@etu.upmc.fr
Received:
15
October
2013
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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