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A Note on Rate of Convergence in Probability to Semicircular Law


 
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1. Title Title of document A Note on Rate of Convergence in Probability to Semicircular Law
 
2. Creator Author's name, affiliation, country Zhidong Bai; Northeast Normal University; China
 
2. Creator Author's name, affiliation, country Jiang Hu; Northeast Normal University; China
 
2. Creator Author's name, affiliation, country Guangming Pan; Nanyang Technological University; Singapore
 
2. Creator Author's name, affiliation, country Wang Zhou; National University of Singapore; Singapore
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) convergence rate, Wigner matrix, Semicircular Law, spectral distribution
 
3. Subject Subject classification Primary 60F15; Secondary 62H99
 
4. Description Abstract In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $O(n^{-1/2})$ when the dimension n tends to infinity.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-11-23
 
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/963
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-963
 
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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