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. doi:10.1214/15-AOP1054. https://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:

URL	URL Type	Description
http://dx.doi.org/10.1214/15-AOP1054	DOI	Article
http://projecteuclid.org/euclid.aop/1474462103	Publisher	Article
https://arxiv.org/abs/1408.3470	arXiv	Discussion Paper

ORCID:

Author	ORCID
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 Agency	Grant 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 Foundation	UNSPECIFIED

Subject Keywords:

Concentration inequalities; Stein’s method; random matrix; noncommutative; exchangeable pairs; coupling; bounded differences; Efron–Stein inequality; trace inequality

Issue or Number:

Classification Code:

MSC2010 subject classifications. Primary 60B20, 60E15; secondary 60G09, 60F10

DOI:

10.1214/15-AOP1054

Record Number:

CaltechAUTHORS:20161103-151616710

Persistent URL:

https://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:

11 Nov 2021 04:50

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