2019/05/20 by Yosuke Aoki, Aoki, Yosuke, Jonathan Bennett +9
Computer Science · Mathematics · #Advanced Topology and Set Theory #Analysis of PDEs (math.AP) #Complexity and Algorithms in Graphs #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1905.07911
openalex publication_date 2019/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quantity which generates a hypercontractivity inequality. Our abstract argument applies to a general Markov semigroup whose generator is a diffusion and satisfies a curvature condition.