{"paper":{"title":"A new special function related to a discrete Gauss-Poisson distribution and some physics of the cell model with Curie-Weiss interactions","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cond-mat.stat-mech","authors_text":"M. A. Shpot, O. A. Dobush","submitted_at":"2024-12-06T21:20:27Z","abstract_excerpt":"Inspired by previous studies in statistical physics [see, in particular, Kozitsky at al., A phase transition in a Curie-Weiss system with binary interactions, Condens. Matter Phys. 23, 23502 (2020)] we introduce a discrete Gauss-Poisson probability distribution function \\begin{equation}\\label{GPD}\\tag{A1} p_{GP}(n ;z,r)=\\left[R(r;z)\\right]^{-1}\\frac{\\mbox{e}^{zn}}{n!}\\,\\mbox{e}^{-\\frac 12\\,rn^2} \\end{equation} with support on $\\mathbb N_0$ and parameters $z\\in\\mathbb R$ and $r\\in\\mathbb R_+$. The probability mass function $p_{GP}(n ;z,r)$ is normalized by the special function $R(r;z)$, given b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.05428","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.05428/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}