Electronic Communications in Probability

Sums of random Hermitian matrices and an inequality by Rudelson

Roberto Oliveira

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Random Hermitian matrices concentration inequalities Khintchine inequalities

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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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