Diffusion Hypercontractivity via Generalized Density Manifold

2019/07/29 by Wuchen Li, Li, Wuchen · 2 citations
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.AP #math.IT

paper · pdf · doi:10.48550/arxiv.1907.12546

arxiv created 2019/10/29 · arxiv updated 2019/10/31

Abstract

We prove a one-parameter family of diffusion hypercontractivity and present the associated Log-Sobolev, Poincare and Talagrand inequalities. A mean-field type Bakry-Emery iterative calculus and volume measure based integration formula (Yano's formula) are presented. Our results are based on the interpolation among divergence functional, generalized diffusion process, and generalized optimal transport metric. As a result, an inequality among Pearson divergence (P), negative Sobolev metric H^-1 and generalized Fisher information functional (I), named PH^-1I inequality, is derived.

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