Outliers in the spectrum of large deformed unitarily invariant models

By Serban Teodor Belinschi, Hari Bercovici, M. Capitaine, Maxime Février. 2012

60 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1deb7e62df26f6bfcc79a5427bf0abe6b25b95bb

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Statistics and Probability

Citations in the corpus

Outlier Eigenvalues for Deformed I.I.D. Random Matrices (2014, background): “Note that motivated by the seminal article of Baik, Ben Arous and Péché [6], previous works are devoted to the study of the outlier eigenvalues of deformed random Hermitian matrix models, see notably [4, 7, 8, 9, 10, 19, 21, 22, 23, 28, 34, 35, 36, 37, 41, 43, 45, 46].”