Non-abelian Littlewood-Offord inequalities
Probability
2015-08-07 v2 Combinatorics
Representation Theory
Abstract
In 1943, Littlewood and Offord proved the first anti-concentration result for sums of independent random variables. Their result has since then been strengthened and generalized by generations of researchers, with applications in several areas of mathematics. In this paper, we present the first non-abelian analogue of Littlewood-Offord result, a sharp anti-concentration inequality for products of independent random variables.
Keywords
Cite
@article{arxiv.1506.01958,
title = {Non-abelian Littlewood-Offord inequalities},
author = {Pham H. Tiep and Van H. Vu},
journal= {arXiv preprint arXiv:1506.01958},
year = {2015}
}
Comments
14 pages Second version. Dependence of the upper bound on the matrix size in the main results has been removed