Analysis and Probability Seminar: “An Upper Bound on the Smallest Singular Value of a Square Random Matrix”

February 20, 2018 (3:00 p.m in Yost 306)

Speaker: Kateryna Tatarko (University of Edmonton)

Abstract: Let A = (a_{ij}) be a square n x n matrix with i.i.d. zero mean and unit variance entries. In a paper by Rudelson and Vershynin it was shown that the upper bound for a smallest singular value s_n(A) is of order n^{-\frac12} with probability close to one under additional assumption on entries of A that $\mathbb{E}a^4_{ij} < \infty$. We remove the assumption on the fourth moment and show the upper bound assuming only $\mathbb{E}a^2_{ij} = 1.$