Spectral measures of powers of random matrices

Elizabeth S Meckes (Case Western Reserve University)
Mark W Meckes (Case Western Reserve University)

Abstract


This paper considers the empirical spectral measure of a power of a random matrix drawn uniformly from one of the compact classical matrix groups. We give sharp bounds on the $L_p$-Wasserstein distances between this empirical measure and the uniform measure on the circle, which show a smooth transition in behavior when the power increases and yield rates on almost sure convergence when the dimension grows. Along the way, we prove the sharp logarithmic Sobolev inequality on the unitary group.


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Pages: 1-13

Publication Date: September 23, 2013

DOI: 10.1214/ECP.v18-2551

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