Transportation-information Inequalities for Markov Processes (ii) : Relations with Other Functional Inequalities
نویسندگان
چکیده
We continue our investigation on the transportation-information inequalities WpI for a symmetric markov process, introduced and studied in [14]. We prove that WpI implies the usual transportation inequalities WpH, 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 W1I (a result due to [14]) 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). keywords: Wasserstein distance; entropy; Fisher information; transport-information inequality; deviation inequality. MSC 2000: 60E15, 60K35; 60G60.
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