Workshop [HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1

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Aug 26, 2021
Thursday

09:30 AM - 10:30 AM

Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
Mireille Capitaine (Centre National de la Recherche Scientifique (CNRS))

September 20, 2010 - September 21, 2010

Workshop Connections for Women: An Introduction to Random Matrices

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Sep 21, 2010
Tuesday

02:00 PM - 03:00 PM		Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices Mireille Capitaine (Centre National de la Recherche Scientifique (CNRS))
Location -- Video Abstract We investigate the asymptotic behavior of the eigenvalues of spiked perturbations of Wigner matrices when the dimension goes to infinity. The perturbation matrix is a deterministic Hermitian matrix whose spectral measure converges to some probability measure with compact support. We assume that this perturbation matrix has a fixed number of fixed eigenvalues (spikes) outside the support of its limiting spectral measure whereas the distance between the other eigenvalues and this support uniformly goes to zero as the dimension goes to infinity. We establish that only a particular subset of the spikes will generate some eigenvalues of the deformed model which will converge to some limiting points outside the support of the limiting spectral measure. This phenomenon can be fully described in terms of free probability involving the subordination function related to the additive free convolution of the limiting spectral measure of the perturbation matrix by a semi-circular distribution. This is a joint work with C. Donati-Martin, D. Féral and M. Février. Supplements -- Show Detail