论文标题
从庞加莱的不平等到非线性基质浓度
From Poincaré Inequalities to Nonlinear Matrix Concentration
论文作者
论文摘要
本文通过简短的概念论点从庞加莱不平等中推论了指数矩阵的浓度。在其他示例中，该理论适用于均匀对数符号随机矢量的基质值函数。证明依赖于庞加莱不平等的亚加性和链条规则的不平等，用于矩阵dirichlet形式的痕迹。它还使用一种对称技术来避免与经典标量参数直接扩展相关的困难。
This paper deduces exponential matrix concentration from a Poincaré inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof relies on the subadditivity of Poincaré inequalities and a chain rule inequality for the trace of the matrix Dirichlet form. It also uses a symmetrization technique to avoid difficulties associated with a direct extension of the classic scalar argument.
