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Fluctuations of Matrix Entries of Lipschitz Functions of Wigner Matrices and Outliers in the Spectrum of Finite Rank Deformations
Probability| Speaker: | Alexander Soshnikov, UC Davis |
| Location: | 1147 MSB |
| Start time: | Wed, Mar 2 2011, 4:10PM |
Description
The first half of the talk will be devoted to the problem of fluctuations of
matrix entries of Lipschitz functions of Wigner random matrices. In the
Gaussian case (GUE/GOE) it
was studied by A.Lytova and L.Pastur in 2009. Their approach significantly
relies on the unitary/orthogonal invariance of the GUE/GOE
ensemble. Using a different approach, I will explain how one can extend the
results of Lytova and Pastur to a sufficiently wide class of Wigner
random matrices.
The second half of the talk will be devoted to the problem of outliers in
the spectrum of finite rank deformations of Wigner random matrices. Our
results generalize earlier results by M.Capitaine, C. Donati-Martin, and D.
Feral.
This is a joint project with Alessandro Pizzo and David Renfrew.