Outliers in the spectrum of large deformed unitarily invariant models

• Serban T. Belinschi ^[2] ; Hari Bercovici ^[3] ; Mireille Capitaine ^[1] ; Maxime Février ^[4]
  1. [1] Toulouse Mathematics Institute

     Toulouse Mathematics Institute

     Arrondissement de Toulouse, Francia

     
  2. [2] Quen's University (Canada)
  3. [3] Indiana University (USA)
  4. [4] Université de Paris-Sud (France)

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 1, 2017, págs. 3571-3625
• Idioma: inglés
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  • 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.