Local stability of the free additive convolution Journal Article


Author(s): Bao, Zhigang; Erdős, László; Schnelli, Kevin
Article Title: Local stability of the free additive convolution
Affiliation IST Austria
Abstract: We prove that the system of subordination equations, defining the free additive convolution of two probability measures, is stable away from the edges of the support and blow-up singularities by showing that the recent smoothness condition of Kargin is always satisfied. As an application, we consider the local spectral statistics of the random matrix ensemble A+UBU⁎A+UBU⁎, where U is a Haar distributed random unitary or orthogonal matrix, and A and B are deterministic matrices. In the bulk regime, we prove that the empirical spectral distribution of A+UBU⁎A+UBU⁎ concentrates around the free additive convolution of the spectral distributions of A and B on scales down to N−2/3N−2/3.
Keywords: Free convolution; Subordination; Local eigenvalue density
Journal Title: Journal of Functional Analysis
Volume: 271
Issue 3
ISSN: 1096-0783
Publisher: Academic Press  
Date Published: 2016-08-01
Start Page: 672
End Page: 719
Sponsor: Partially supported by ERC Advanced Grant RANMAT No. 338804. Supported by ERC Advanced Grant RANMAT No. 338804. We thank an anonymous referee for many useful comments and remarks, and bringing references [6] ; [12] to our attention.
URL:
DOI: 10.1016/j.jfa.2016.04.006
Open access: yes (repository)
IST Austria Authors
  1. László Erdős
    102 Erdős
  2. Zhigang Bao
    7 Bao