From Poincar\'e Inequalities to Nonlinear Matrix Concentration

De Huang; Joel A. Tropp

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arXiv · 2006.16561

From Poincar\'e Inequalities to Nonlinear Matrix Concentration

De Huang·Joel A. Tropp

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Abstract

This paper deduces exponential matrix concentration from a Poincar\'e 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 Poincar\'e 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.

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De Huang, Joel A. Tropp. 2020-06-30. From Poincar\'e Inequalities to Nonlinear Matrix Concentration. https://arxiv.org/abs/2006.16561

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