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Free probability of type B and asymptotics of finite-rank perturbations of random matrices

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arxiv 1509.08841 v1 pith:ORWSJB5A submitted 2015-09-29 math.PR math.OA

D. Shlyakhtenko This is my paper · ORCID
classification math.PRmath.OA
keywords freematricesperturbationsrandomtypeadditiveanalysisappearance
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We show that finite rank perturbations of certain random matrices fit in the framework of infinitesimal (type B) asymptotic freeness. This can be used to explain the appearance of free harmonic analysis (such as subordination functions appearing in additive free convolution) in computations of outlier eigenvalues in spectra of such matrices.

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  1. Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrum

    math.PR 2019-08 conditional novelty 6.0 of 10

    Arizmendi and Celestino extend Collins-Hasebe-Sakuma spectral formulas to a broad class of matrix-embeddable polynomials in cyclically monotone variables, with applications to limiting eigenvalues of random matrices w...

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