Author(s):

Lee, Jioon; Schnelli, Kevin

Article Title: 
Edge 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 Wigner matrix and V 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 of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the rescaled distribution of the extremal eigenvalues is given by the TracyWidom distribution F1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.

Keywords: 
Random matrix; edge universality

Journal Title:

Reviews in Mathematical Physics

Volume: 
27

Issue 
8

ISSN:

0129055X

Publisher:

World Scientific Publishing

Date Published:

20150901

Start Page: 
Article number: 1550018

URL: 

DOI: 
10.1142/S0129055X1550018X

Open access: 
yes (repository) 