Open Access
July 2015 Subordination for the sum of two random matrices
V. Kargin
Ann. Probab. 43(4): 2119-2150 (July 2015). DOI: 10.1214/14-AOP929


This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original matrices. We estimate the error terms in this relation and in the subordination relation for the traces of the resolvents. This allows us to prove a local limit law for eigenvalues and a delocalization result for eigenvectors of the sum of two random matrices. In addition, we use subordination to determine the limit of the largest eigenvalue for the rank-one deformations of unitary-invariant random matrices.


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V. Kargin. "Subordination for the sum of two random matrices." Ann. Probab. 43 (4) 2119 - 2150, July 2015.


Received: 1 March 2013; Revised: 1 January 2014; Published: July 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1320.60022
MathSciNet: MR3353823
Digital Object Identifier: 10.1214/14-AOP929

Primary: 60B20

Keywords: delocalization , local limit law , random matrices , small-rank matrix deformations , Subordination

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 4 • July 2015
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