Bulk universality for deformed wigner matrices Journal Article

Author(s): Lee, Jioon; Schnelli, Kevin; Stetler, Ben; Yau, Horngtzer
Article Title: Bulk universality for deformed wigner matrices
Affiliation IST Austria
Abstract: We consider N×N random matrices of the form H = W + V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues ofW and V are typically of the same order. For a large class of diagonal matrices V , we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.
Keywords: Local semicircle law; Universality; Random matrix
Journal Title: Annals of Probability
Volume: 44
Issue 3
ISSN: 0091-1798
Publisher: Institute of Mathematical Statistics  
Date Published: 2016-01-01
Start Page: 2349
End Page: 2425
DOI: 10.1214/15-AOP1023
Notes: J.C. was supported in part by National Research Foundation of Korea Grant 2011-0013474 and TJ Park Junior Faculty Fellowship. K.S. was supported by ERC Advanced Grant RANMAT, No. 338804, and the "Fund for Math." B.S. was supported by NSF GRFP Fellowship DGE-1144152. H.Y. was supported in part by NSF Grant DMS-13-07444 and Simons investigator fellowship. We thank Paul Bourgade, László Erd ̋ os and Antti Know- les for helpful comments. We are grateful to the Taida Institute for Mathematical Sciences and National Taiwan Universality for their hospitality during part of this research. We thank Thomas Spencer and the Institute for Advanced Study for their hospitality during the academic year 2013–2014.
Open access: yes (repository)
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