Efron–Stein inequalities for random matrices

Daniel Paulin; Lester Mackey; Joel A. Tropp

doi:10.1214/15-AOP1054

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Home > Journals > Ann. Probab. > Volume 44 > Issue 5 > Article

September 2016 Efron–Stein inequalities for random matrices

Daniel Paulin, Lester Mackey, Joel A. Tropp

Ann. Probab. 44(5): 3431-3473 (September 2016). DOI: 10.1214/15-AOP1054

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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.

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Daniel Paulin. Lester Mackey. Joel A. Tropp. "Efron–Stein inequalities for random matrices." Ann. Probab. 44 (5) 3431 - 3473, September 2016. https://doi.org/10.1214/15-AOP1054

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Received: 1 August 2014; Revised: 1 August 2015; Published: September 2016

First available in Project Euclid: 21 September 2016

zbMATH: 1378.60025

MathSciNet: MR3551202

Digital Object Identifier: 10.1214/15-AOP1054

Subjects:

Primary: 60B20 , 60E15

Secondary: 60F10 , 60G09

Keywords: bounded differences , Concentration inequalities , coupling , Efron–Stein inequality , Exchangeable pairs , noncommutative , Random matrix , Stein’s method , trace inequality

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Vol.44 • No. 5 • September 2016

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Daniel Paulin, Lester Mackey, Joel A. Tropp "Efron–Stein inequalities for random matrices," The Annals of Probability, Ann. Probab. 44(5), 3431-3473, (September 2016)

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