Hunter Spink: Anti-concentration of random walks on model-theoretic definable sets

(Joint with Jacob Fox, Matthew Kwan) Classical anti-concentration results show “random walks in ℝ^d with BIG independent steps can’t concentrate in balls much better than they can concentrate on individual points”. Model-theoretic definable sets include boolean combinations of subsets of ℝ^d defined using equalities and inequalities of arbitrary compositions of polynomials, e^x, ln(x) and analytic functions restricted to compact boxes. For example, the intersection of e^{sin(1/(1+(xyz)2))+x2y}+zy ≥ 0 and xyz=5 in ℝ³. In this talk, I will discuss recent results which show “random walks in ℝ^d with ARBITRARY independent steps can’t concentrate in definable sets not containing line segments much better than they can concentrate on individual points”. Time permitting, I will discuss how these results extend to other groups like GL_d(ℝ).

This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.