文章基本信息

标题：Scalar Poincaré implies matrix Poincaré
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作者：Ankit Garg ; Tarun Kathuria ; Nikhil Srivastava 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2021
卷号：26
页码：1-4
DOI：10.1214/21-ECP371
语种：English
出版社：Electronic Communications in Probability
摘要：We prove that every reversible Markov semigroup which satisfies a Poincaré inequality satisfies a matrix-valued Poincaré inequality for Hermitian d×d matrix valued functions, with the same Poincaré constant. This generalizes recent results [ABY19, Kat20] establishing such inequalities for specific semigroups and consequently yields new matrix concentration inequalities. The short proof follows from the spectral theory of Markov semigroup generators.
关键词：46N30; 60B20; matrix concentration; Poincaré inequality