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

Probability 2026-02-19 v2

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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Cite

@article{arxiv.2510.25869,
  title  = {A note on the Littlewood-Offord problem for discrete log-concave distributions},
  author = {Arnaud Marsiglietti and James Melbourne},
  journal= {arXiv preprint arXiv:2510.25869},
  year   = {2026}
}

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15 pages