{
  "abstract": "We derive a weighted Kirchhoff diffusion on a smooth Riemannian open book as a scaling limit of regime-switching Brownian motions on boundaryless manifolds. The pages are compact Riemannian manifolds sharing a common boundary manifold and inducing the same metric on the binding, while their second fundamental forms and interior geometries may differ. For each $\\varepsilon>0$, we regularize the metric in an $o(\\varepsilon)$ collar, pass to smooth doubles of the pages, run Brownian motion on each double, and allow the page label to switch in a collar of width $\\varepsilon$ at rates \\(q_\\varepsilon(r)Q_{ij},\\) where $Q$ is an arbitrary irreducible finite-state Markov generator with invariant law $π$, while \\(q_\\eps\\) is bounded and supported on an \\(\\eps\\) collar. Denoting \\(Θ_\\eps\\) the total mass of \\(q_\\eps\\) and \\(Ξ_\\eps\\) its second raw moment, we prove that, if \\(Θ_\\varepsilon\\to\\infty\\) and \\(Ξ_\\varepsilon\\to0\\), then the glued processes converge, from every deterministic sequence of starting points, to Brownian motion with weigthed Kirchhoff interface conditions. No reversibility of $Q$, pointwise scaling ansatz for $q_\\varepsilon$, or first-moment condition is required. Furthermore, we show that the second fundamental form of the pages contributes no additional interface term: curvature remains only through the bulk Laplace--Beltrami operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02570",
  "author_total": 1,
  "authors": [
    {
      "name": "Leonardo Marconi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8d84edj0gmbwh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02570",
  "fulltext_url": null,
  "id": "8d84edj0gmbwh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02570",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220397979",
  "pdf_url": "https://arxiv.org/pdf/2610.02570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8d84edj0gmbwh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02570"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Fast Switching Near a Smooth Interface: A Curvature-Universal Kirchhoff Limit",
  "title_text": "Fast Switching Near a Smooth Interface: A Curvature-Universal Kirchhoff Limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/8d84edj0gmbwh",
  "venue": "arXiv",
  "versions": []
}