From Poincaré inequalities to nonlinear matrix concentration

The talk is based on the paper, From Poincaré inequalities to nonlinear matrix concentration by De Huang and Joel A. Tropp, arXiv link.

Abstract (from the paper)

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.