Local law of addition of random matrices on optimal scale Journal Article

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: 1432-0916
Publisher: Springer  
Date Published: 2017-02-01
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.
DOI: 10.1007/s00220-016-2805-6
Open access: yes (OA journal)
IST Austria Authors
  1. László Erdős
    109 Erdős
  2. Zhigang Bao
    7 Bao