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November 2017 Outliers in the spectrum of large deformed unitarily invariant models
Serban T. Belinschi, Hari Bercovici, Mireille Capitaine, Maxime Février
Ann. Probab. 45(6A): 3571-3625 (November 2017). DOI: 10.1214/16-AOP1144


We characterize the possible outliers in the spectrum of large deformed unitarily invariant additive and multiplicative models, as well as the eigenvectors corresponding to them. We allow both the nondeformed unitarily invariant model and the perturbation matrix to have nontrivial limiting eigenvalue distributions and spiked outliers in their spectrum. The free subordination functions play a key role in this analysis.


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Serban T. Belinschi. Hari Bercovici. Mireille Capitaine. Maxime Février. "Outliers in the spectrum of large deformed unitarily invariant models." Ann. Probab. 45 (6A) 3571 - 3625, November 2017.


Received: 1 May 2015; Revised: 1 April 2016; Published: November 2017
First available in Project Euclid: 27 November 2017

zbMATH: 06838102
MathSciNet: MR3729610
Digital Object Identifier: 10.1214/16-AOP1144

Primary: 60B20
Secondary: 46L54

Keywords: deformed unitarily invariant models , free probability and free subordination , random matrices , spikes and outliers

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 6A • November 2017
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