Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 245, Issue 2, Pages 379-389Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2007.01.003
Keywords
concentration of measure; concentration inequalities; Stein's method; semigroup method; Haar measure; random walk; mixing time
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We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of eigenvalues of sums of random Hermitian matrices, with possible applications in free probability. The advantage over existing techniques is that the new method can deal with functions that are non-Lipschitz or even discontinuous with respect to the usual metrics. (c) 2007 Elsevier Inc. All rights reserved.
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