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Efron–Stein inequalities for random matrices

Paulin, Daniel and Mackey, Lester and Tropp, Joel A. (2016) Efron–Stein inequalities for random matrices. Annals of Probability, 44 (5). pp. 3431-3473. ISSN 0091-1798. http://resolver.caltech.edu/CaltechAUTHORS:20161103-151616710

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Abstract

This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron–Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1214/15-AOP1054DOIArticle
http://projecteuclid.org/euclid.aop/1474462103PublisherArticle
https://arxiv.org/abs/1408.3470arXivDiscussion Paper
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Additional Information:© 2016 Institute of Mathematical Statistics. Received August 2014; revised August 2015. Supported by ONR awards N00014-08-1-0883 and N00014-11-1002, AFOSR award FA9550-09-1-0643, and a Sloan Research Fellowship.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-08-1-0883
Office of Naval Research (ONR)N00014-11-1002
Air Force Office of Scientific Research (AFOSR)FA9550-09-1-0643
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Concentration inequalities; Stein’s method; random matrix; noncommutative; exchangeable pairs; coupling; bounded differences; Efron–Stein inequality; trace inequality
Classification Code:MSC2010 subject classifications. Primary 60B20, 60E15; secondary 60G09, 60F10
Record Number:CaltechAUTHORS:20161103-151616710
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161103-151616710
Official Citation:Paulin, Daniel; Mackey, Lester; Tropp, Joel A. Efron–Stein inequalities for random matrices. Ann. Probab. 44 (2016), no. 5, 3431--3473. doi:10.1214/15-AOP1054. http://projecteuclid.org/euclid.aop/1474462103
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71728
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Nov 2016 23:23
Last Modified:03 Nov 2016 23:23

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