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Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation


 
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1. Title Title of document Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation
 
2. Creator Author's name, affiliation, country Laszlo Erdos; LMU-University of Munich; Germany
 
2. Creator Author's name, affiliation, country Jose A. Ramirez; Universidad de Costa Rica; Costa Rica
 
2. Creator Author's name, affiliation, country Benjamin Schlein; University of Bonn; Germany
 
2. Creator Author's name, affiliation, country Horng-Tzer Yau; Harvard University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Wigner random matrix, Dyson sine kernel
 
3. Subject Subject classification 15A52, 82B44
 
4. Description Abstract We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance $N^{-3/4+\beta}$ for some positive $\beta>0$. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Geramn Research Coucil, NSF
 
7. Date (YYYY-MM-DD) 2010-05-01
 
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/768
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-768
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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