{
  "abstract": "Understanding the connection between galaxies and dark matter halos is a central challenge in modern cosmology. The Halo Occupation Distribution (HOD) framework provides a widely used statistical description of how galaxies populate dark matter halos, enabling precise modelling of galaxy clustering. A common assumption in standard HOD models is that the number of satellite galaxies follows a Poisson distribution at fixed halo mass. In this work, we revisit this assumption and introduce the Conway-Maxwell-Poisson (CMP) distribution as a minimal extension of of the Poisson model, which add a single parameter, $ν$, to explore sub- and super-Poisson behaviour. We derive analytical approximations for the CMP expectation parameter $λ$ and develop a numerical scheme that smoothly connects small- and large-$λ$ regimes, achieving $\\sim5\\%$ accuracy for $0.5 < ν< 2$. Using the \\texttt{HODDIES} package, we study the impact of non-Poisson satellite occupations on mock galaxy catalogues and clustering statistics. Variations in the variance of the satellite occupation significantly affect small-scale clustering, producing deviations of up to $10\\%$ in projected clustering and $5\\%$ in the monopole and quadrupole. We further investigate higher-order statistics using counts-in-cylinders (CiC) and the tree-level galaxy bispectrum. CiC statistics are highly sensitive to changes in the variance, with variations up to $\\sim30\\%$, while the tree-level galaxy bispectrum (in the Sugiyama basis) is only weakly affected ($<2\\%$ up to $k_\\mathrm{max} = 0.3$). These results suggest that non-Poisson satellite statistics are important for small-scale analyses, but should have a limited impact on cosmological constraints from power spectrum and bispectrum measurements using large scales $k_\\mathrm{max} < 0.3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.28644",
  "author_total": 1,
  "authors": [
    {
      "name": "Antoine Rocher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bh3h0rt4p286k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.28644",
  "fulltext_url": null,
  "id": "bh3h0rt4p286k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.28644",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "openalex",
      "3103|Galaxies: Formation, Evolution, Phenomena"
    ]
  ],
  "openalex": "W7162680311",
  "pdf_url": "https://arxiv.org/pdf/2605.28644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh3h0rt4p286k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2605.28644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.28644"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering",
  "title_text": "Exploring non-Poisson satellite occupation in HOD models and its impact on 2- and 3-point galaxy clustering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/bh3h0rt4p286k",
  "venue": "arXiv",
  "versions": []
}