Scalar Poincaré implies matrix Poincaré
نویسندگان
چکیده
We prove that every reversible Markov semigroup which satisfies a Poincaré inequality matrix-valued for Hermitian d×d matrix valued functions, with the same constant. This generalizes recent results [ABY19, Kat20] establishing such inequalities specific semigroups and consequently yields new concentration inequalities. The short proof follows from spectral theory of generators.
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2021
ISSN: ['1083-589X']
DOI: https://doi.org/10.1214/21-ecp371