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Limiting spectral distribution of sum of unitary and orthogonal matrices


 
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1. Title Title of document Limiting spectral distribution of sum of unitary and orthogonal matrices
 
2. Creator Author's name, affiliation, country Anirban Basak; Stanford University; United States
 
2. Creator Author's name, affiliation, country Amir Dembo; Stanford University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrices, limiting spectral distribution, Haar measure, Brown measure, free convolution, Stieltjes transform, Schwinger-Dyson equation.
 
3. Subject Subject classification 46L53, 60B10, 60B20.
 
4. Description Abstract We show that the empirical eigenvalue measure for sum of $d$ independent Haar distributed $n$-dimensional unitary matrices, converge for $n \rightarrow \infty$ to the Brown measure of the free sum of $d$ Haar unitary operators. The same applies for independent Haar distributed $n$-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes transform of $T_n$ that is made in [Guionnet, Krishnapur, Zeitouni; Theorem 1].
 
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7. Date (YYYY-MM-DD) 2013-08-10
 
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/2466
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2466
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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