{
  "abstract": "We prove universal Gaussian and stable fluctuation limits for one-dimensional long-range first-passage percolation with edge times $\\|x-y\\|^αω_{x,y}$. The positive i.i.d. weights satisfy $\\mathbb{P}(ω\\le t)=t^{θ+o(1)}$ as $t\\downarrow0$ and $\\mathbb{E}(ω^ζ)<\\infty$ for some $θ,ζ>0$. For $α>1+2/θ$, the passage time $T(0,n)$ has a positive deterministic linear growth rate $μ$. For $α>1+3/θ$, we establish a Gaussian central limit theorem with linear asymptotic variance, a functional version, and limit theorems for geodesic hop and cut point counts. For $1+2/θ<α<1+3/θ$, assuming a regularly varying lower tail, we obtain a totally left-skewed stable limit with index $β=θ(α-1)-1$ and an explicit scale, together with convergence to a spectrally negative stable Lévy process in the Skorokhod $M_1$ topology. The proof constructs i.i.d. blocks between hubs through which every crossing geodesic must pass. A spread-out comparison metric makes this regeneration available for every $ζ>0$, even when the edge law has infinite mean. The key estimate identifies the exact left-tail asymptotic of the centered block reward, generated by a single fast long edge. A monotone within-block approximation yields the functional stable limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37180",
  "author_total": 2,
  "authors": [
    {
      "name": "Shirshendu Chatterjee"
    },
    {
      "name": "Partha S. Dey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hdnn7v1mzrbk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37180",
  "fulltext_url": null,
  "id": "5hdnn7v1mzrbk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37180",
  "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": "W7224099763",
  "pdf_url": "https://arxiv.org/pdf/2610.37180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hdnn7v1mzrbk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37180"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Scaling limit and universality for one-dimensional long-range first-passage metric in the linear-growth regime",
  "title_text": "Scaling limit and universality for one-dimensional long-range first-passage metric in the linear-growth regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/5hdnn7v1mzrbk",
  "venue": "arXiv",
  "versions": []
}