Event Series
Event Type
Seminar
Thursday, October 31, 2019 2:00 PM
Vishesh Jain (MIT)

Let s_n(M_n) denote the smallest singular value of an nxn random matrix M_n. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood--Offord theory or net arguments) for proving statements of the following form for quite general random matrix models: there exist constants c, C > 0 such that for all \eta \geq 0, Pr(s_n(M_n) \leq \eta) \lesssim n^{C}\eta + \exp(-\Omega(n^{c})). In several cases of interest, our results strengthen those of Tao and Vu obtained using inverse Littlewood--Offord theory.