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arXiv · 1707.01085

Optimal Littlewood-Offord inequalities in groups

T. Juškevičius·G. Šemetulskis
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Abstract

We prove several Littlewood-Offord type inequalities for arbitrary groups. In groups having elements of finite order the worst case scenario is provided by the simple random walk on a certain cyclic subgroup. The inequalities we obtain are optimal if the underlying group contains an element of certain order. It turns out that for torsion-free groups Erd\H{o}s's bound still holds. Our results strengthen and generalize some very recent results by Tiep and Vu.

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T. Juškevičius, G. Šemetulskis. 2017-07-04. Optimal Littlewood-Offord inequalities in groups. https://doi.org/10.1007/s00493-018-3845-7

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