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Recursive overlap Bernoulli distributions and an entropy concavity conjecture
Abstract
We introduce a family of recursively generated finite probability distributions obtained from left and right embeddings with overlaps. The construction interpolates between the classical binomial distribution and the non-overlapping Bernoulli product distribution. We derive explicit formulas for the expectation, variance, and the generating function of higher moments, and formulate a conjecture asserting that the Shannon entropy is concave. The conjecture is proved in the two extremal cases and supported by symbolic computations for numerous overlap sequences.
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BibTeX
@misc{neunhauserer2026recursive,
title = {{Recursive overlap Bernoulli distributions and an entropy concavity conjecture}},
author = {Jörg Neunhäuserer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05546},
eprint = {2609.05546},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05546},
}
RIS
TY - UNPB
TI - Recursive overlap Bernoulli distributions and an entropy concavity conjecture
AU - Jörg Neunhäuserer
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.05546
UR - https://arxiv.org/abs/2609.05546
AB - We introduce a family of recursively generated finite probability distributions obtained from left and right embeddings with overlaps. The construction interpolates between the classical binomial distribution and the non-overlapping Bernoulli product distribution. We derive explicit formulas for the expectation, variance, and the generating function of higher moments, and formulate a conjecture asserting that the Shannon entropy is concave. The conjecture is proved in the two extremal cases and supported by symbolic computations for numerous overlap sequences.
ER -