The Annals of Probability

Bulk universality for deformed Wigner matrices

Ji Oon Lee, Kevin Schnelli, Ben Stetler, and Horng-Tzer Yau

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Abstract

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 $N$.

Article information

Source
Ann. Probab., Volume 44, Number 3 (2016), 2349-2425.

Dates
Received: June 2014
Revised: February 2015
First available in Project Euclid: 16 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1463410044

Digital Object Identifier
doi:10.1214/15-AOP1023

Mathematical Reviews number (MathSciNet)
MR3502606

Zentralblatt MATH identifier
1346.15037

Subjects
Primary: 15B52: Random matrices 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Random matrix local semicircle law universality

Citation

Lee, Ji Oon; Schnelli, Kevin; Stetler, Ben; Yau, Horng-Tzer. Bulk universality for deformed Wigner matrices. Ann. Probab. 44 (2016), no. 3, 2349--2425. doi:10.1214/15-AOP1023. https://projecteuclid.org/euclid.aop/1463410044


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