Author(s):

Bao, Zhigang; Erdős, László; Schnelli, Kevin

Article Title: 
Local law of addition of random matrices on optimal scale

Affiliation 
IST Austria 
Abstract: 
The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.

Journal Title:

Communications in Mathematical Physics

Volume: 
349

Issue 
4

ISSN:

14320916

Publisher:

Springer

Date Published:

20170201

Start Page: 
947

End Page:

990

Copyright Statement: 
CC BY 4.0

Sponsor: 
Z. Bao, L. Erdős and K.Schnelli were supported by ERC Advanced Grant RANMAT No. 338804.

URL: 

DOI: 
10.1007/s0022001628056

Open access: 
yes (OA journal) 