OUTLIERS IN THE SPECTRUM OF LARGE DEFORMED UNITARILY INVARIANT MODELS

• 成果类型: Article
• 署名作者: Belinschi, Serban T.; Bercovici, Hari; Capitaine, Mireille; Fevrier, Maxime
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Queens University - Canada; Romanian Academy; University of Bucharest; Institute of Mathematics of the Romanian Academy; Indiana University System; Indiana University Bloomington; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1144
• 发表日期: 2017
• 页码: 3571-3625
• 关键词: strong asymptotic freeness; LARGEST EIGENVALUE; free convolution; wigner matrices; deformations

摘要

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.