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A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices


 
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1. Title Title of document A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
 
2. Creator Author's name, affiliation, country László Erdős; LMU-University of Munich; 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, Mehta, Universality
 
3. Subject Subject classification 15A52; 82B44
 
4. Description Abstract Recently we proved that  the  eigenvalue correlation functions of a general class of random matrices converge,  weakly with respect to the energy, to  the corresponding ones of  Gaussian matrices. Tao and Vu gave a proof that for the special case of Hermitian Wigner matrices the convergence  can be strengthened to vague  convergence at any  fixed energy in the bulk. In this article we comment on this result in the context of the universality conjectures of Mehta. We show that this theorem is  an immediate corollary of our earlier results. Indeed,  a more general form of this theorem also follows directly from our previous work.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF, DFG
 
7. Date (YYYY-MM-DD) 2012-04-10
 
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/1779
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1779
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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