# Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities

Abstract : We continue our investigation on the transportation-information inequalities $W_pI$ for a symmetric markov process, introduced and studied in \cite{GLWY}. We prove that $W_pI$ implies the usual transportation inequalities $W_pH$, then the corresponding concentration inequalities for the invariant measure $\mu$. We give also a direct proof that the spectral gap in the space of Lipschitz functions for a diffusion process implies $W_1I$ (a result due to \cite{GLWY}) and a Cheeger type's isoperimetric inequality. Finally we exhibit relations between transportation-information inequalities and a family of functional inequalities (such as $\Phi$-log Sobolev or $\Phi$-Sobolev).
Keywords :
Type de document :
Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-00360854
Contributeur : Arnaud Guillin <>
Soumis le : jeudi 12 février 2009 - 13:39:42
Dernière modification le : mercredi 23 janvier 2019 - 10:28:25
Document(s) archivé(s) le : mardi 8 juin 2010 - 20:44:58

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glww200109.pdf
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• HAL Id : hal-00360854, version 1
• ARXIV : 0902.2101

### Citation

Arnaud Guillin, Christian Léonard, Feng-Yu Wang, Liming Wu. Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities. 2009. ⟨hal-00360854⟩

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