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On fluctuation of the outliers in the spectrum of finite-rank deformations of large random matrices

4:00 pm Thursday, November 3, 2011
Alexander Soshnikov (UC Davis)

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices. In this talk, I will show how one can reduce this problem to the problem about the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. The latter problem can be tackled by a combination of standard probabilistic techniques (such as CLT for martingale differences) and resolvent techniques.

The talk will be accessible to non-experts in random matrices.

The talk is based on the results of the three preprints written this spring in collaboration with Sean O'Rourke, Alessandro Pizzo, and David Renfrew:

"On Finite Rank Deformations of Wigner Matrices" arXiv:1103.3731 math.PR (to appear in Annales de l'Institut Henri Poincare),

"Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices" arXiv:1103.1170 math.PR,

and

"Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries" arXiv:1106.0320 math.PR.

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