{
  "abstract": "We study conditional fluctuations of smooth mean-field systems on a torus with endogenous symmetric stable common jumps of index $0<α<1$. A positive-strip estimate makes empirical Poisson acceptance errors negligible at the sampling scale. The conditional laws given the full Poisson master converge in probability to a centered Gaussian kernel in a negative Sobolev path space. In dimension one, quantile coupling preserves this limit for microscopic marks with relative tail remainder $O(x^{-ρ})$, $ρ>α/2$. A quantified second-order tail expansion gives the endogenous rank response: it shifts the conditional Gaussian mean at criticality and, when nonzero, dominates sampling below criticality. We also identify a separate stable-to-Brownian transition for the rank error. Finally, in a translation model, rank and clock couplings give the same microscopic laws. The rank coupling has a functional Gaussian limit. The clock coupling has no diverging additive path normalization at the limiting center.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01391",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandre Autran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2tw6swtw16w69.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01391",
  "fulltext_url": null,
  "id": "2tw6swtw16w69",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01391",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7215708355",
  "pdf_url": "https://arxiv.org/pdf/2610.01391",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2tw6swtw16w69.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.01391",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01391"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Conditional Fluctuations of Mean-Field Systems with Stable Common Noise",
  "title_text": "Conditional Fluctuations of Mean-Field Systems with Stable Common Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/2tw6swtw16w69",
  "venue": "arXiv",
  "versions": []
}