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On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries


 
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1. Title Title of document On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries
 
2. Creator Author's name, affiliation, country Radoslaw Adamczak; University of Warsaw; Poland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random matrix, Marchenko-Pastur law, circular law, log-concave measures
 
3. Subject Subject classification 15B52
 
4. Description Abstract In the first part of the article we prove limit theorems of Marchenko-Pastur type for the average spectral distribution of random matrices with dependent entries satisfying a weak law of large numbers, uniform bounds on moments and a martingale like condition investigated previously by Goetze and Tikhomirov. Examples include log-concave unconditional distributions on the space of matrices. In the second part we specialize to random matrices with independent isotropic unconditional log-concave rows for which (using the Tao-Vu replacement principle) we prove the circular law.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) MNiSW, Foundation for Polish Science
 
7. Date (YYYY-MM-DD) 2011-06-02
 
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/899
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-899
 
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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