{
  "abstract": "We study the emergence of a mutual giant component in a multiplex network comprised of two one-dimensional long-range networks on a lattice. The probability that two nodes on one lattice, with a distance $r$ between them, are connected with an edge falls algebraically with distance as $Cr^{-(1+σ)}$, where $0 < σ< 1$ and $0 < C \\leq 1$. A mutual giant component exists if $C > C_c^{\\mathrm{mul}}$, where $C_c^{\\mathrm{mul}}(σ)$ is a critical value of $C$ that is dependent on $σ$. We find rigorous lower bounds on $C_c^{\\mathrm{mul}}$, and a tree approximation whose estimate of $C_c^{\\mathrm{mul}}$ agrees with simulations within 0.6% for $σ\\leq 0.5$. The multiplex network is significantly less stable than the single network case, as is evident by the larger value of $C_c^{\\mathrm{mul}}$, which is up to 2.4 times the single-layer value. Our simulations indicate that the order of the transition depends on $σ$. For $σ\\leq 0.35$ the mutual giant component collapses abruptly, in a first-order phase transition, while for $σ\\geq 0.4$ the transition is continuous. When the dependency links connect random pairs of nodes, the transition is first order for all $σ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10097",
  "author_total": 4,
  "authors": [
    {
      "name": "Adar Sharabi"
    },
    {
      "name": "Amir Bashan"
    },
    {
      "name": "Sergey V. Buldyrev"
    },
    {
      "name": "Guy Amit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6060zby59jwe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10097",
  "fulltext_url": null,
  "id": "f6060zby59jwe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10097",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7220928615",
  "pdf_url": "https://arxiv.org/pdf/2610.10097",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6060zby59jwe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.10097",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10097"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Percolation on interdependent one-dimensional long-range networks",
  "title_text": "Percolation on interdependent one-dimensional long-range networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/f6060zby59jwe",
  "venue": "arXiv",
  "versions": []
}