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On the spectrum of sum and product of non-hermitian random matrices


 
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1. Title Title of document On the spectrum of sum and product of non-hermitian random matrices
 
2. Creator Author's name, affiliation, country Charles Bordenave; CNRS and University of Toulouse
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) generalized eigenvalues, non-hermitian random matrices, spherical law
 
3. Subject Subject classification 60B20 ; 47A10; 15A18
 
4. Description Abstract In this note, we revisit the work of T. Tao and V. Vu on large non-hermitian random matrices with independent and identically distributed (i.i.d.) entries with mean zero and unit variance. We prove under weaker assumptions that the limit spectral distribution of sum and product of non-hermitian random matrices is universal. As a byproduct, we show that the generalized eigenvalues distribution of two independent matrices converges almost surely to the uniform measure on the Riemann sphere.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-02-12
 
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/1606
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1606
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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