Special Seminar

Come join us Wednesday January 31, 2018 at 12 pm in RM 507, Professor Konstantin Tikhomirov (Princeton) will be giving a special lecture about “Invertibility and Spectrum of Random Matrices: A Convex-Geometric Approach”.

Abstract

Convex-geometric methods, involving random projection operators and coverings, have been successfully used in the study of the largest and smallest singular value, delocalization of eigenvectors, and in establishing the limiting spectral distribution for certain random matrix models. Among further applications of those methods in computer science and statistics are restricted invertibility (dimension reduction), as well as approximation of covariance matrices of multidimensional distributions. Conversely, random linear operators play a very important role in geometric functional analysis. In this talk, I will discuss some recent results (by my collaborators and myself) within the theory of random matrices, focusing on invertibility of square non-Hermitian random matrices (with applications to numerical analysis and the study of the limiting spectral distribution of directed d-regular graphs) and approximation of co-variance matrices (in particular, a strengthening of the Bai-Yin theorem.

Mathematics Hall, Room 507

Wednesday January 31, 2018 at 12 pm

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