{
  "abstract": "We investigate reflected diffusion in a bounded domain subject to two independent, competing stopping mechanisms: an exponentially distributed bulk lifetime of rate $p$ and a surface reaction triggered when the boundary local time exceeds an independent exponential threshold of rate $q$. Denoting by $T$ the stopping time and by $L$ the acquired boundary local time at stopping, we derive their marginal distributions, joint Laplace transform, and complete hierarchy of mixed moments. These statistics are determined by the splitting probability $ϕ$ that surface reaction occurs before bulk decay. In particular, we establish the identity $p\\expect{T}+q\\expect{L}=1$ and show that the cumulative risk $pT+qL$ is exponentially distributed with unit rate. We further obtain equivalent representations of $ϕ$ in terms of the Robin-Laplacian and the generalized Steklov spectra. Explicit results for a three-dimensional ball reveal how competing rates $p,q$ control $ϕ$ and the $(T,L)$ statistics. Monte Carlo simulations test the universal cumulative-risk law.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05247",
  "author_total": 1,
  "authors": [
    {
      "name": "Yilin Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jy7jzy8rckx8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05247",
  "fulltext_url": null,
  "id": "3jy7jzy8rckx8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05247",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7211898100",
  "pdf_url": "https://arxiv.org/pdf/2609.05247",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jy7jzy8rckx8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2609.05247",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05247"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Diffusion under competing bulk and surface stopping mechanisms",
  "title_text": "Diffusion under competing bulk and surface stopping mechanisms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/3jy7jzy8rckx8",
  "venue": "arXiv",
  "versions": []
}