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Coefficientwise Hankel-total positivity from a universal cumulant lifting — arXiv:2611.01172

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01172
License (as archived): CC0-1.0
Archived: 2026-11-03T18:47:43.918Z
SHA-256 of the archived text: d006755cf9cf299f26c71fba7e20ff5ff7e4b9a0cdca3ab30e1a2fe767495c38
Stable URL of this page: https://metraipolis.com/documento/dc_679451b66ea6

How to cite

Coefficientwise Hankel-total positivity from a universal cumulant lifting — arXiv:2611.01172 — arXiv (en), https://arxiv.org/abs/2611.01172 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_679451b66ea6 (Metraipolis archive dc_679451b66ea6, sha256 d006755cf9cf299f26c71fba7e20ff5ff7e4b9a0cdca3ab30e1a2fe767495c38)

BibTeX

@misc{dc679451b66ea6,
  title = {Coefficientwise Hankel-total positivity from a universal cumulant lifting — arXiv:2611.01172},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01172},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_679451b66ea6; sha256 d006755cf9cf299f26c71fba7e20ff5ff7e4b9a0cdca3ab30e1a2fe767495c38},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01172. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Using probabilistic methods, we establish universal cumulant lifting criteria for Stieltjes and Hamburger moment sequences. In the Stieltjes case, we characterize coefficientwise Hankel total positivity after convolution with every initial moment sequence by requiring each once-shifted cumulant sequence to be Stieltjes. We also prove equivalence with the numerical moment property at every nonnegative intensity. In the Hamburger case, we use twice-shifted cumulants to obtain coefficientwise-positive leading Hankel determinants, a degree bound, an explicit highest-degree component, and drift invariance. We work with formal series and require neither exponential moments nor moment determinacy. We establish composition, binomial-convolution, and substitution results, and apply them to implicit equations and autonomous differential equations, tree and forest families, and lognormal compound-Poisson moments in a unified approach. From known moment sequences, we obtain general coefficientwise Hankel-totally positive families containing the classical Bessel, Lah, and Laguerre polynomials. We not only give new proofs of coefficientwise Hankel-total positivity of many combinatorial polynomials, but also prove coefficientwise Hankel total positivity for the component polynomials of functional digraphs confirming a conjecture of Sokal and establish fixed-shape Schläfli--Gessel--Seo polynomials positivity supporting another conjecture of Sokal.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO) ; Classical Analysis and ODEs (math.CA); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2611.01172 — 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 2026-11-03T18:15:07.749Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).