Geodesic
Modified logarithmic Sobolev inequalities for canonical ensembles
Fathi, Max1 
1 LPMA, University Paris 6, France.
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 544-559

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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’s model.

Reçu le :
DOI : 10.1051/ps/2015004
Classification : 60K35, 82B21
Keywords: Modified logarithmic Sobolev inequalities, spin system, coarse-graining

Fathi, Max 1

1 LPMA, University Paris 6, France. 
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     author = {Fathi, Max},
     title = {Modified logarithmic {Sobolev} inequalities for canonical ensembles},
     journal = {ESAIM: Probability and Statistics},
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     publisher = {EDP-Sciences},
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     year = {2015},
     doi = {10.1051/ps/2015004},
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     zbl = {1336.60187},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2015004/}
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Fathi, Max. Modified logarithmic Sobolev inequalities for canonical ensembles. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 544-559. doi: 10.1051/ps/2015004

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