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### Fluctuations of Matrix Entries of Lipschitz Functions of Wigner Matrices and Outliers in the Spectrum of Finite Rank Deformations

**Mathematical Physics & Probability**

Speaker: | Alexander Soshnikov, UC Davis |

Location: | 1147 MSB |

Start time: | Wed, Mar 2 2011, 4:10PM |

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.