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Spectral measures of powers of random matrices


 
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1. Title Title of document Spectral measures of powers of random matrices
 
2. Creator Author's name, affiliation, country Elizabeth S Meckes; Case Western Reserve University; United States
 
2. Creator Author's name, affiliation, country Mark W Meckes; Case Western Reserve University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Uniform random matrices; spectral measure; Wasserstein distance; logarithmic Sobolev inequality
 
3. Subject Subject classification 60B20; 60B15; 60E15; 60F05
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) U.S. National Science Foundation, American Institute of Mathematics
 
7. Date (YYYY-MM-DD) 2013-09-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2551
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2551
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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