An upper bound on the smallest singular value of a square random matrix

2018/05/14 by Tatarko, Kateryna · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1805.05018

Abstract

Let A = (a_ij) be a square n× n matrix with i.i.d. zero mean and unit variance entries. Rudelson and Vershynin showed 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 𝔼a⁴₁₁ < ∞. We remove the assumption on the fourth moment and show the upper bound assuming only 𝔼a²₁₁ = 1.

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