A Caltech Library Service

From Poincaré inequalities to nonlinear matrix concentration

Huang, De and Tropp, Joel A. (2021) From Poincaré inequalities to nonlinear matrix concentration. Bernoulli, 27 (3). pp. 1724-1744. ISSN 1350-7265. doi:10.3150/20-BEJ1289.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Tropp, Joel A.0000-0003-1024-1791
Additional Information:© 2021 ISI/BS. Received: 1 June 2020; Revised: 1 October 2020; Published: August 2021. First available in Project Euclid: 10 May 2021. Ramon Van Handel offered valuable feedback on a preliminary version of this work, and we are grateful to him for the proof of Proposition 2.4. DH was funded by NSF grants DMS-1907977 and DMS-1912654. JAT gratefully acknowledges funding from ONR awards N00014-17-12146 and N00014-18-12363, and he would like to thank his family for their support in these difficult times.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-17-12146
Office of Naval Research (ONR)N00014-18-12363
Subject Keywords:concentration inequality, functional inequality, Markov process, matrix concentration, Poincaré inequality, semigroup
Issue or Number:3
Classification Code:2010 Mathematics Subject Classification. Primary: 60B20, 46N30. Secondary: 60J25, 46L53
Record Number:CaltechAUTHORS:20201218-154430753
Persistent URL:
Official Citation:De Huang. Joel A. Tropp. "From Poincaré inequalities to nonlinear matrix concentration." Bernoulli 27 (3) 1724-1744, August 2021.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107217
Deposited By: George Porter
Deposited On:21 Dec 2020 15:40
Last Modified:09 Jun 2021 20:01

Repository Staff Only: item control page