{
  "abstract": "The rough response calculus for the rotationally marked SLE welding law gives a closed Weil--Petersson energy but does not by itself give a process on rough weldings. For $0<κ\\leq4$, we prove that this form is quasi-regular in the natural topology of circle homeomorphisms and therefore generates a canonical diffusion reversible with respect to the SLE welding probability. The proof constructs a compact form nest from inverse arc masses. We identify the generator as $-D^*D$ and prove absolute $L^2$ convergence of its Fourier expansion on the response cylinder core, together with the Fukushima decomposition. A common Fourier noise and planar estimates preventing boundary collapse yield a second quasi-regular realization by normalized Jordan welding triples. The diffusion is irreducible and converges strongly in $L^2$ to equilibrium. For $0<κ<4$, the complement of the conformally removable welding locus has zero capacity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00407",
  "author_total": 1,
  "authors": [
    {
      "name": "Chunhao Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jk02q0tp02bq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00407",
  "fulltext_url": null,
  "id": "3jk02q0tp02bq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00407",
  "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.CV"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7216520882",
  "pdf_url": "https://arxiv.org/pdf/2610.00407",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jk02q0tp02bq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00407",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00407"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The canonical SLE-reversible Weil--Petersson response diffusion",
  "title_text": "The canonical SLE-reversible Weil--Petersson response diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/3jk02q0tp02bq",
  "venue": "arXiv",
  "versions": []
}