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From Poincaré Inequalities to Nonlinear Matrix Concentration

Huang, De and Tropp, Joel A. (2020) From Poincaré Inequalities to Nonlinear Matrix Concentration. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20201218-154430753

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Abstract

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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2006.16561arXivDiscussion Paper
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Additional Information: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 grant DMS-1613861. 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.
Funders:
Funding AgencyGrant Number
NSFDMS-1613861
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
Classification Code:2010 Mathematics Subject Classification. Primary: 60B20, 46N30. Secondary: 60J25, 46L53
Record Number:CaltechAUTHORS:20201218-154430753
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201218-154430753
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107217
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 Dec 2020 15:40
Last Modified:21 Dec 2020 15:40

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