Yuanyuan Xu: Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrix

Time: Tue 2019-10-29 15.15 - 16.15

Lecturer: Yuanyuan Xu, KTH

Location: F11, KTH

Abstract

We consider \(N\) by \(N\) deformed Wigner random matrices of the form \(X=H+A\), where \(H\) is a real symmetric or complex Hermitian Wigner matrix and A is a deterministic real bounded diagonal matrix. We prove a universal Central Limit Theorem for the linear eigenvalue statistics of \(X\) on all mesoscopic scales both in the spectral bulk and at regular edges where the global eigenvalue density vanishes as a square root, respectively. This is a joint work with Yiting Li and Kevin Schnelli. 

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