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Products of Independent non-Hermitian Random Matrices


 
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1. Title Title of document Products of Independent non-Hermitian Random Matrices
 
2. Creator Author's name, affiliation, country Sean O'Rourke; Rutgers University; United States
 
2. Creator Author's name, affiliation, country Alexander B. Soshnikov; University of California Davis; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrices; Circular law
 
3. Subject Subject classification 60B20
 
4. Description Abstract We consider the product of a finite number of non-Hermitian random matrices with i.i.d. centered entries of growing size. We assume that the entries have a finite moment of order bigger than two. We show that the empirical spectral distribution of the properly normalized product converges, almost surely, to a non-random, rotationally invariant distribution with compact support in the complex plane. The limiting distribution is a power of the circular law.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation
 
7. Date (YYYY-MM-DD) 2011-11-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/954
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-954
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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