Edge universality for deformed Wigner matrices Journal Article

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 Tracy-Widom 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: 0129-055X
Publisher: World Scientific Publishing  
Date Published: 2015-09-01
Start Page: Article number: 1550018
DOI: 10.1142/S0129055X1550018X
Open access: yes (repository)
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