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The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition

✍ Scribed by Daniel W. Stroock; Boguslaw Zegarlinski


Publisher
Springer
Year
1992
Tongue
English
Weight
970 KB
Volume
144
Category
Article
ISSN
0010-3616

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Generalization of an Inequality by Talag
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We show that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6, 587 600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities. Conversely, Talagrand's inequality implies a logarithmic Sobolev inequality if the density of the measure i