Outliers in the spectrum of large deformed unitarily invariant models

Serban Teodor Belinschi; Hari Bercovici; Mireille Capitaine; Maxime Fevrier

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arXiv · 1412.4916

Outliers in the spectrum of large deformed unitarily invariant models

Serban Teodor Belinschi·Hari Bercovici·Mireille Capitaine·Maxime Fevrier

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Abstract

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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Serban Teodor Belinschi, Hari Bercovici, Mireille Capitaine, Maxime Fevrier. 2014-12-16. Outliers in the spectrum of large deformed unitarily invariant models. https://arxiv.org/abs/1412.4916

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