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May 2016 Bulk universality for deformed Wigner matrices
Ji Oon Lee, Kevin Schnelli, Ben Stetler, Horng-Tzer Yau
Ann. Probab. 44(3): 2349-2425 (May 2016). DOI: 10.1214/15-AOP1023


We consider $N\times N$ 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 of $W$ 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 $N$.


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Ji Oon Lee. Kevin Schnelli. Ben Stetler. Horng-Tzer Yau. "Bulk universality for deformed Wigner matrices." Ann. Probab. 44 (3) 2349 - 2425, May 2016.


Received: 1 June 2014; Revised: 1 February 2015; Published: May 2016
First available in Project Euclid: 16 May 2016

zbMATH: 1346.15037
MathSciNet: MR3502606
Digital Object Identifier: 10.1214/15-AOP1023

Primary: 15B52 , 60B20 , 82B44

Keywords: Local semicircle law , Random matrix , Universality

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 3 • May 2016
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