From Poincar\'e Inequalities to Nonlinear Matrix Concentration
Probability
2021-01-08 v2
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.
Cite
@article{arxiv.2006.16561,
title = {From Poincar\'e Inequalities to Nonlinear Matrix Concentration},
author = {De Huang and Joel A. Tropp},
journal= {arXiv preprint arXiv:2006.16561},
year = {2021}
}