Open Access
May 2014 Matrix concentration inequalities via the method of exchangeable pairs
Lester Mackey, Michael I. Jordan, Richard Y. Chen, Brendan Farrell, Joel A. Tropp
Ann. Probab. 42(3): 906-945 (May 2014). DOI: 10.1214/13-AOP892


This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein’s method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoeffding, Bernstein, Khintchine and Rosenthal. The same technique delivers bounds for sums of dependent random matrices and more general matrix-valued functions of dependent random variables.


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Lester Mackey. Michael I. Jordan. Richard Y. Chen. Brendan Farrell. Joel A. Tropp. "Matrix concentration inequalities via the method of exchangeable pairs." Ann. Probab. 42 (3) 906 - 945, May 2014.


Published: May 2014
First available in Project Euclid: 26 March 2014

zbMATH: 1294.60008
MathSciNet: MR3189061
Digital Object Identifier: 10.1214/13-AOP892

Primary: 60B20 , 60E15
Secondary: 60F10 , 60G09

Keywords: Concentration inequalities , Exchangeable pairs , Moment inequalities , noncommutative , Random matrix , Stein’s method

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 3 • May 2014
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