{
  "abstract": "We study the collective dynamics of independent particles that diffuse outside a spherical surface, on which they are replicated with a prescribed catalytic rate. In spatial dimensions three and higher, the transient nature of diffusion creates a competition between autocatalytic branching and escape to infinity, leading to three distinct regimes: subcritical (finite limiting population), critical (algebraic growth), and supercritical (exponential growth). The rotational symmetry of the domain and an explicit form of the single-particle diffusion propagator allow us to fully investigate the time evolution of the population size, including the mean population size, variance, higher-order moments, as well as the whole distribution. In particular, we obtain an explicit form of the distribution at long times and describe a slow, power-law approach to this steady-state limit. We further extend the steady-state analysis to general exterior domains using the Dirichlet-to-Neumann operator, which determines the critical catalytic rate and reveals how boundary geometry affects the population-size distribution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.14133",
  "author_total": 1,
  "authors": [
    {
      "name": "Denis S. Grebenkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17jvhz1azppkv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.14133",
  "fulltext_url": null,
  "id": "17jvhz1azppkv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.14133",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7164814499",
  "pdf_url": "https://arxiv.org/pdf/2606.14133",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/17jvhz1azppkv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2606.14133",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.14133"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Diffusion-Driven Surface Autocatalysis in Exterior Domains",
  "title_text": "Diffusion-Driven Surface Autocatalysis in Exterior Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/17jvhz1azppkv",
  "venue": "arXiv",
  "versions": []
}