{
  "abstract": "We investigate the power-law decay of the survival probability of a Brownian particle diffusing in an infinite planar wedge whose two sides are partially reactive and described by Robin boundary conditions. We employ matched asymptotic analysis to relate the long-time asymptotics to a stationary harmonic Robin problem near the apex. This approach determines the persistence exponent for arbitrary opening angles and yields the prefactor explicitly for the family of wedges with $α=π/n$ ($n=1,2,\\ldots$). A simple extension of the apex prefactor to arbitrary angles is conjectured and supported numerically. This asymptotic behavior describes the crossover to the well-known result for perfectly absorbing wedges. As immediate applications, we also deduce the long-time behavior of the probability density function of the boundary local time on wedge sides, as well as the probability density function of the associated first-crossing time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02665",
  "author_total": 1,
  "authors": [
    {
      "name": "Denis S. Grebenkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dwq8e24gj0evx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02665",
  "fulltext_url": null,
  "id": "dwq8e24gj0evx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02665",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7207615833",
  "pdf_url": "https://arxiv.org/pdf/2609.02665",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dwq8e24gj0evx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02665",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Survival in a partially reactive wedge",
  "title_text": "Survival in a partially reactive wedge",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/dwq8e24gj0evx",
  "venue": "arXiv",
  "versions": []
}