Anti-concentration of inhomogeneous random walks

TL;DR

This paper characterizes anti-concentration phenomena for inhomogeneous random walks in non-abelian groups and extends classical probabilistic bounds to these more complex algebraic structures.

Contribution

It introduces a new characterization for anti-concentration in non-abelian groups and generalizes classical bounds to these settings.

Findings

Extended Erdos-Littlewood-Offord bounds to non-abelian groups

Provided a new characterization for anti-concentration in inhomogeneous random walks

Applicable to a broad class of non-abelian group settings

Abstract

We provide a characterization for anti-concentration of inhomogeneous random walks in non-abelian groups. In application we extend the classical bounds by Erdos-Littlewood-Offord and Sarkozy-Szemeredi to non-abelian settings.