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- W1664971939 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)." @default.
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- W1664971939 date "2009-02-01" @default.
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- W1664971939 title "Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities" @default.
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