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

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dc.creatorGuillin, Arnaud
dc.creatorLeonard, Christian
dc.creatorWang, Feng-Yu
dc.creatorWu, Liming
dc.date2009-02-12
dc.date.accessioned2026-07-07T12:40:56Z
dc.date.available2026-07-07T12:40:56Z
dc.descriptionWe 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 $μ$. 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 $Φ$-log Sobolev or $Φ$-Sobolev).
dc.identifierhttps://arxiv.org/abs/0902.2101
dc.identifierhttp://arxiv.org/abs/0902.2101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219603
dc.subjectProbability
dc.subject60E15, 60K35; 60G60
dc.titleTransportation-information inequalities for Markov processes (II) : relations with other functional inequalities
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