Metraipolis › archive › dc_bc56577256cf

Recursive overlap Bernoulli distributions and an entropy concavity conjecture — arXiv:2609.05546

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05546
License (as archived): CC0-1.0
Archived: 2026-10-16T15:01:47.199Z
SHA-256 of the archived text: 33b31f67e298d012c304e2d901b07330e9331bd194232e1d6c7551848e9169c6
Stable URL of this page: https://metraipolis.com/documento/dc_bc56577256cf

How to cite

Recursive overlap Bernoulli distributions and an entropy concavity conjecture — arXiv:2609.05546 — arXiv (en), https://arxiv.org/abs/2609.05546 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bc56577256cf (Metraipolis archive dc_bc56577256cf, sha256 33b31f67e298d012c304e2d901b07330e9331bd194232e1d6c7551848e9169c6)

BibTeX

@misc{dcbc56577256cf,
  title = {Recursive overlap Bernoulli distributions and an entropy concavity conjecture — arXiv:2609.05546},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05546},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bc56577256cf; sha256 33b31f67e298d012c304e2d901b07330e9331bd194232e1d6c7551848e9169c6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05546. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.IT).
Categorie arXiv: Information Theory (cs.IT) ; Dynamical Systems (math.DS).
Pagina del lavoro: https://arxiv.org/abs/2609.05546 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:48:50.692Z dalla pagina https://arxiv.org/catchup/math.IT/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).