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Article Dans Une Revue Annals of Probability Année : 2017

OUTLIERS IN THE SPECTRUM OF LARGE DEFORMED UNITARILY INVARIANT MODELS

Résumé

In this paper 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 non-deformed unitarily invariant model and the perturbation matrix to have non-trivial limiting spectral measures and spiked outliers in their spectrum. We uncover a remarkable new phenomenon: a single spike can generate asymptotically several outliers in the spectrum of the deformed model. The free subordination functions play a key role in this analysis.
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Dates et versions

hal-01095551 , version 1 (15-12-2014)
hal-01095551 , version 2 (20-03-2015)

Identifiants

Citer

Serban Belinschi, Hari Bercovici, Mireille Capitaine, Maxime Fevrier. OUTLIERS IN THE SPECTRUM OF LARGE DEFORMED UNITARILY INVARIANT MODELS. Annals of Probability, 2017, 45 (6A), pp.3571-3625. ⟨10.1214/16-AOP1144⟩. ⟨hal-01095551v2⟩
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