Tight lower bounds for anti-concentration of Rademacher sums and Tomaszewski's counterpart problem

Lawrence Hollom, Julien Portier

In this paper we prove that $\mathbb{P}(|X|\ge \sqrt{\text{Var}(X)})\ge 7/32$ for every finite Rademacher sum $X$, confirming a conjecture by Hitczenko and Kwapie{ń} from 1994,…