An efficient way to discretize a sphere

Combinatorics Seminar
Friday, September 15, 2023 - 3:15pm for 1 hour (actually 50 minutes)
Skiles 308
Galyna Livshyts – Georgia Tech – glivshyts6@math.gatech.edu
Tom Kelly

We discuss small-ball probability estimates of the smallest singular value of a rather general ensemble of random matrices which we call “inhomogeneous”. One of the novel ingredients of our family of universality results is an efficient discretization procedure, applicable under unusually mild assumption. Most of the talk will focus on explaining the ideas behind the proof of the first ingredient. Partially based on the joint work with Tikhomirov and Vershynin, and an ongoing joint work with Fernandez and Tatarko. We will also mention a related work on the cube minimal dispersion, joint with Litvak.