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:

00911798

Publisher:

Institute of Mathematical Statistics

Date Published:

20160101

Start Page: 
2349

End Page:

2425

URL: 

DOI: 
10.1214/15AOP1023

Notes: 
J.C. was supported in part by National Research Foundation of Korea Grant 20110013474 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 DGE1144152.
H.Y. was supported in part by NSF Grant DMS1307444 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) 