{
  "abstract": "Self-intersection local times serve as the Hamiltonian in the Gibbs measure of continuous polymer models, for which the end-to-end distance is a key quantity. We study multiple self-intersection local times of Volterra Gaussian bridges, \\emph{i.e.}, Volterra Gaussian processes conditioned on their final location $a$, as $\\|a\\|\\to\\infty$. For $d$-dimensional $(2,ζ)$-locally nondeterministic processes with $ζ\\in(0,2/d)$, we prove that these local times exist in every $L^p$. Under two further conditions on the kernel, the $p$-th moment of the $m$-multiple self-intersection local time of the bridge is of exact order $\\|a\\|^{-γ}$ for every integer $p\\geqslant1$, with $γ=p(m-1)(2-ζd)/(2-ζ)$. In the plane, for kernels $k(t-s)$ with $k(0)\\neq0$ and under strong local nondeterminism, we restrict the double self-intersection local time to $\\{t_2-t_1\\geqslant\\|a\\|^{-α}\\}$, $α>0$, and establish a phase transition: its expectation decays like $\\exp(-c\\|a\\|^{2-α})$, converges to an explicit positive limit, or grows logarithmically, for $α<2$, $α=2$ and $α>2$ respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35769",
  "author_total": 2,
  "authors": [
    {
      "name": "Olga Izyumtseva"
    },
    {
      "name": "Wasiur R. KhudaBukhsh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xg3ehg4ehw7t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35769",
  "fulltext_url": null,
  "id": "2xg3ehg4ehw7t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35769",
  "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-ph"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7224001713",
  "pdf_url": "https://arxiv.org/pdf/2610.35769",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xg3ehg4ehw7t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35769",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35769"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Self-intersection local times of Volterra Gaussian bridges with large end-to-end distance",
  "title_text": "Self-intersection local times of Volterra Gaussian bridges with large end-to-end distance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/2xg3ehg4ehw7t",
  "venue": "arXiv",
  "versions": []
}