{
  "abstract": "We investigate robustness under percolation in the degree-driven spatial preferential attachment model. Consider a profile that is regularly varying with exponent $-δ$, where $δ>1$, and an attachment rule with asymptotic slope $γ\\in(0,1)$. Jacob and Mörters (Ann. Probab. 45 (2017)) proved robustness when $$ δ\\left(\\frac1γ-1\\right)<1. $$ We prove the converse in the strict regime: if $$ δ\\left(\\frac1γ-1\\right)>1, $$ then sufficiently strong Bernoulli vertex thinning destroys the giant component. In particular, the strict robustness boundary coincides with that of the age-dependent random connection model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29853",
  "author_total": 2,
  "authors": [
    {
      "name": "Peter Gracar"
    },
    {
      "name": "Christian Mönch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/am8jgv9fsjpnf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29853",
  "fulltext_url": null,
  "id": "am8jgv9fsjpnf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29853",
  "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",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7223242377",
  "pdf_url": "https://arxiv.org/pdf/2610.29853",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/am8jgv9fsjpnf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29853",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29853"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Spatial preferential attachment models: robustness revisited",
  "title_text": "Spatial preferential attachment models: robustness revisited",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/am8jgv9fsjpnf",
  "venue": "arXiv",
  "versions": []
}