A note on the Littlewood-Offord problem for discrete log-concave distributions

Arnaud Marsiglietti; James Melbourne

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arXiv · 2510.25869

A note on the Littlewood-Offord problem for discrete log-concave distributions

Arnaud Marsiglietti·James Melbourne

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Abstract

We present an extension of the famous Littlewood-Offord problem when Bernoulli distributions are replaced with discrete log-concave distributions. A variant of the Littlewood-Offord problem for arithmetic progressions, as well as an entropic version, is also discussed. Along the way, we recover and extend a result of Madiman and Woo (2015) on the entropy power inequality for discrete uniform distributions.

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Arnaud Marsiglietti, James Melbourne. 2025-10-29. A note on the Littlewood-Offord problem for discrete log-concave distributions. https://arxiv.org/abs/2510.25869

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