The Annals of Probability
- Ann. Probab.
- Volume 43, Number 4 (2015), 2119-2150.
Subordination for the sum of two random matrices
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.
Ann. Probab., Volume 43, Number 4 (2015), 2119-2150.
Received: March 2013
Revised: January 2014
First available in Project Euclid: 3 June 2015
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Kargin, V. Subordination for the sum of two random matrices. Ann. Probab. 43 (2015), no. 4, 2119--2150. doi:10.1214/14-AOP929. https://projecteuclid.org/euclid.aop/1433341328