arXiv Analytics

Sign in

arXiv:math/0508518 [math.PR]AbstractReferencesReviewsResources

Concentration of Haar measures, with an application to random matrices

Sourav Chatterjee

Published 2005-08-26, updated 2007-01-23Version 3

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.

Comments: 12 pages. To appear in J. Funct. Anal
Categories: math.PR, math.MG
Subjects: 60E15, 28C10, 46L54, 15A52
Related articles: Most relevant | Search more
arXiv:1201.6036 [math.PR] (Published 2012-01-29)
On Hàjek - Rényi type inequality and application
arXiv:math/0405355 [math.PR] (Published 2004-05-18)
Deviation inequality for monotonic Boolean functions with application to a number of k-cycles in a random graph
arXiv:1103.3683 [math.PR] (Published 2011-03-18, updated 2012-05-23)
Exact bounds on the truncated-tilted mean, with applications

Links

Toolbox