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 Electronic Communications in Probability > Vol. 15(2010) > Paper 19 open journal systems 


Sums of random Hermitian matrices and an inequality by Rudelson

Roberto I. Oliveira, IMPA


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.


Full text: PDF

Pages: 203-212

Published on: June 8, 2010
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Electronic Communications in Probability. ISSN: 1083-589X