论文标题
标量庞加莱暗示矩阵庞加莱
Scalar Poincaré Implies Matrix Poincaré
论文作者
论文摘要
我们证明，满足Poincaré不平等的每个可逆Markov Semigroup都满足了Hermitian的矩阵值得元素的不平等，$ d \ times d $矩阵有价值的功能，具有相同的Poincaré常数。这概括了最近的结果[Aoun等。 2019年，凯瑟里亚（Kathuria）2019年]确定特定半群的这种不平等现象，因此产生了新的矩阵浓度不平等。简短的证明来自马尔可夫半群发电机的光谱理论。
We prove that every reversible Markov semigroup which satisfies a Poincaré inequality satisfies a matrix-valued Poincaré inequality for Hermitian $d\times d$ matrix valued functions, with the same Poincaré constant. This generalizes recent results [Aoun et al. 2019, Kathuria 2019] 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.
