STA 290 Seminar: Alexander Soshnikov (UC Davis)

Statistics Seminar: STA 290

Thursday, March 15th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)

Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)

Speaker:  Alexander Soshnikov (Dept. Mathematics, UC Davis)

Title:        On outliers in the spectrum of finite rank deformations of Wigner matrices

Abstract: In the first part of the talk I will discuss our recent results on the limiting distribution of the largest eigenvalues of finite rank deformations of Wigner random matrices.

The second part of the talk will be devoted to the problem of fluctuation matrix entries of regular functions of Wigner matrices. In particular, I will explain how these two problems are related.

Our results generalize earlier works by M.Capitaine, C. Donati-Martin, and D. Feral, A. Lytova and L. Pastur, and Z.D. Bai and G.M. Pan.

The talk is based on four recent papers/preprints:


1) "On Finite Rank Deformations of Wigner Matrices" available at arXiv:1103.3731 math.PR, to appear in the Annales de l'Institut Henri Poincare (B) Probabilites et Statistiques, (joint with Alessandro Pizzo and David Renfrew)


2) "On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries" available at arXiv:1104.1663 math.PR, to appear in the Journal of Theoretical Probability,

(joint with Sean O'Rourke and David Renfrew)


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

Journal of Statistical Physics, v.146, No. 3, 550-591, (2012)

(joint with Alessandro Pizzo and David Renfrew),


4) "On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations" (joint with David Renfrew).