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A note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices


 
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1. Title Title of document A note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices
 
2. Creator Author's name, affiliation, country Sandrine Dallaporta; Institut de Mathématiques de Toulouse
 
2. Creator Author's name, affiliation, country Van H. Vu; Department of Mathematics, Rutgers
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random matrices ; eigenvalue counting function ; Central Limit Theorem ; Four Moment Theorem ; localization
 
3. Subject Subject classification 60B20 ; 60F05
 
4. Description Abstract The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson, and its extension to large families of Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erd?s, Yau and Yin.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) AFORS ; NSF
 
7. Date (YYYY-MM-DD) 2011-06-22
 
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/1634
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1634
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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