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2013 Spectral measures of powers of random matrices
Elizabeth Meckes, Mark Meckes
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Electron. Commun. Probab. 18: 1-13 (2013). DOI: 10.1214/ECP.v18-2551

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.

Citation

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Elizabeth Meckes. Mark Meckes. "Spectral measures of powers of random matrices." Electron. Commun. Probab. 18 1 - 13, 2013. https://doi.org/10.1214/ECP.v18-2551

Information

Accepted: 23 September 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1310.60003
MathSciNet: MR3109633
Digital Object Identifier: 10.1214/ECP.v18-2551

Subjects:
Primary: 60B20
Secondary: 60B15, 60E15, 60F05

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