A note on the Littlewood-Offord problem for discrete log-concave distributions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911452946759680 |
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| author | Marsiglietti, Arnaud Melbourne, James |
| author_facet | Marsiglietti, Arnaud Melbourne, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the Littlewood-Offord problem for discrete log-concave distributions Marsiglietti, Arnaud Melbourne, James Probability 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. |
| title | A note on the Littlewood-Offord problem for discrete log-concave distributions |
| topic | Probability |
| url | https://arxiv.org/abs/2510.25869 |