{
  "abstract": "We study inhomogeneous long-range first-passage percolation on $\\mathbb{Z}^d$ with edge passage times $\\lVert x-y\\rVert^αω_{xy}/(V_xV_y)$, where vertex weights have polynomial upper-tail exponent $γ$ and edge noises have polynomial lower-tail exponent $θ$ at zero. The model interpolates between long-range first-passage percolation and scale-free percolation and exhibits competition between reusable heavy-vertex hubs and pair-specific small-noise bridges. We conjecture an eight-regime phase diagram, organized into five growth phases governed by $q_{\\rm hub}=d/γ$ and $q_{\\rm edge}=d/θ$. For $T_n=T(0,\\lceil nx\\rceil)$, we prove upper bounds of the conjectured order in every regime and matching lower bounds in phases I and II. Specifically, $T_n=0$ a.s. when $α<q_{\\rm hub}\\vee q_{\\rm edge}$, while $T_n=Θ_{\\mathbb{P}}(1)$ when $q_{\\rm hub}\\vee q_{\\rm edge}<α<2q_{\\rm hub}$. In the edge-dominated intermediate regime, $T_n=O_{\\mathbb{P}}((\\log n)^{Δ_{\\rm III}+\\varepsilon})$, where $Δ_{\\rm III}=\\log 2/\\log(2q_{\\rm edge}/α)$. The two power-law regimes satisfy $T_n=O_{\\mathbb{P}}(n^{α-2q_{\\rm hub}+\\varepsilon})$ and $T_n=O_{\\mathbb{P}}(n^{α-2q_{\\rm edge}+\\varepsilon})$, and the linear regime satisfies $T_n=O_{\\mathbb{P}}(n)$. All upper bounds are constructive, based on hub-chain and binary edge-bridge multiscale constructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20422",
  "author_total": 3,
  "authors": [
    {
      "name": "Shirshendu Chatterjee"
    },
    {
      "name": "Partha S. Dey"
    },
    {
      "name": "Daecheol Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74frnfn2z5vss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20422",
  "fulltext_url": null,
  "id": "74frnfn2z5vss",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20422",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213610149",
  "pdf_url": "https://arxiv.org/pdf/2609.20422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74frnfn2z5vss.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20422"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Inhomogeneous Long-Range First-Passage Percolation in a Random Vertex Environment",
  "title_text": "Inhomogeneous Long-Range First-Passage Percolation in a Random Vertex Environment",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/74frnfn2z5vss",
  "venue": "arXiv",
  "versions": []
}