Tomas Juškevičius, Vilnius University

Abstract

The goal of the talk is to talk about some recent developments regarding the Littlewood-Offord problem. We shall consider this problem in the group theoretic setting. The first results of this type were obtained by Griggs (1993) in cyclic groups and very recently by Tiep and Vu (2015) in certain matrix groups. We shall present an optimal version of such inequalities in arbitary groups. Many variations of the Littlewood-Offord problem have been explored during the years - the so called inverse version (pioneered by Tao and Vu), the resilience version (Bandeira, Ferber and Kwan) etc. In this talk we shall talk about a yet another extension - a non-uniform version of the Littlewood-Offord problem. To be more precise, we shall bound the probability of hitting a particular vector $v$ by a sum of independent symmetric steps in terms of the length of $v$.

The talk is based on joint work with G. Šemetulskis and D. Dzindzalieta.