Electronic Communications in Probability

Sums of random Hermitian matrices and an inequality by Rudelson

Roberto Oliveira

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Abstract

We give a new, elementary proof of a key inequality used by Rudelson in the derivation of his well-known bound for random sums of rank-one operators. Our approach is based on Ahlswede and Winter's technique for proving operator Chernoff bounds. We also prove a concentration inequality for sums of random matrices of rank one with explicit constants.

Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 19, 203-212.

Dates
Accepted: 8 June 2010
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465243962

Digital Object Identifier
doi:10.1214/ECP.v15-1544

Mathematical Reviews number (MathSciNet)
MR2653725

Zentralblatt MATH identifier
1228.60017

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Keywords
Random Hermitian matrices concentration inequalities Khintchine inequalities

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Oliveira, Roberto. Sums of random Hermitian matrices and an inequality by Rudelson. Electron. Commun. Probab. 15 (2010), paper no. 19, 203--212. doi:10.1214/ECP.v15-1544. https://projecteuclid.org/euclid.ecp/1465243962


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