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Fluctuations and Large Deviations for Extreme Eigenvalues of Deformed Random Matrices

Connections for Women: An Introduction to Random Matrices September 20, 2010 - September 21, 2010

September 20, 2010 (03:30pm PDT - 04:30pm PDT)

Speaker(s): Mylene Maida

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Abstract

This is joint work with F.~Benaych Georges and Alice Guionnet. We consider a model of matrices with well-known spectrum (deterministic with converging spectral measure, Wigner, Wishart etc.) and add a random perturbation with finite rank and delocalized eigenvectors. We get so called spiked or deformed models which lately received quite a lot of attention. We investigate the asymptotic behavior of their extreme eigenvalues, in particular their fluctuations and large deviations properties.

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