{
  "abstract": "In this paper we introduce the model of Percolative MDLA (PMDLA) on $\\mathbb{Z}^2$ which engulfs the entire occupied percolation component of each particle that reaches the aggregate. We prove a phase transition of finite time explosion, as a function of the particle density $λ$, where the critical value equals $λ_c=-\\log(1-p_c^{\\rm site}(\\mathbb{Z}^2))$. Below $λ_c$, the process is nonexplosive and has a linear upper bound on its radius. For $2/3<λ<λ_c$, it also has a linear lower bound on the growth rate. Above $λ_c$, an infinite component is swallowed in finite time a.s. At $λ_c$, every update is finite, but the updates accumulate in finite time, causing a blowup. Excluding criticality, the results are generalized to all higher dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19622",
  "author_total": 3,
  "authors": [
    {
      "name": "Eviatar B. Procaccia"
    },
    {
      "name": "Haoyu Wang"
    },
    {
      "name": "Yuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7v69dapq7mefr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19622",
  "fulltext_url": null,
  "id": "7v69dapq7mefr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19622",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7222003523",
  "pdf_url": "https://arxiv.org/pdf/2610.19622",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7v69dapq7mefr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19622",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19622"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Percolative MDLA: phase transition and critical behaviour",
  "title_text": "Percolative MDLA: phase transition and critical behaviour",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/7v69dapq7mefr",
  "venue": "arXiv",
  "versions": []
}