{
  "abstract": "Let $L^x$ be the total local time of one-dimensional super-Brownian motion with $(1+β)$-stable branching mechanism, $0<β<1$. We prove that $\\{x\\in\\mathbb R:L^x>0\\}$ is almost surely a bounded open interval $(\\mathsf L,\\mathsf R)$ and that \\[ h_L(\\mathsf L)=h_L(\\mathsf R)=1+\\frac{2}β \\] almost surely, where $h_L$ denotes the pointwise Hölder exponent. Thus the pointwise $γ$-Hölder condition holds at both endpoints for every $γ<1+2/β$ and fails for every $γ>1+2/β$. The same conclusions hold under the canonical excursion measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00690",
  "author_total": 3,
  "authors": [
    {
      "name": "Jieliang Hong"
    },
    {
      "name": "Du Yang"
    },
    {
      "name": "Junyan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/416bdm5ypy6fp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00690",
  "fulltext_url": null,
  "id": "416bdm5ypy6fp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00690",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7206162791",
  "pdf_url": "https://arxiv.org/pdf/2609.00690",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/416bdm5ypy6fp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00690",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00690"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Boundary behavior and optimal pointwise Hölder exponent of the total local time of $(1+β)$-stable super-Brownian motion",
  "title_text": "Boundary behavior and optimal pointwise Hölder exponent of the total local time of (1+β)-stable super-Brownian motion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/416bdm5ypy6fp",
  "venue": "arXiv",
  "versions": []
}