{
  "abstract": "[Kosygina et al. 2023] showed that the rescaled polynomially self-repelling walk does not converge to any Brownian motion perturbed at extrema (BMPE). Motivated by this result, we introduce an explicit candidate for the scaling limit, the polynomially self-repelling motion (PSRM), and study its properties. The construction relies on a new family of continuous stochastic flows, called polynomially self-repelling flows, introduced in [Yu 2026]. A key ingredient in relating the limiting process of the rescaled walk to the PSRM is a joint Ray-Knight theorem for rescaled local time processes, extending the classical Ray-Knight theorems of [Tóth 1996].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38591",
  "author_total": 1,
  "authors": [
    {
      "name": "Yaolin Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmd2qkath608q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38591",
  "fulltext_url": null,
  "id": "bmd2qkath608q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38591",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38591",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmd2qkath608q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38591",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38591"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Polynomially Self-repelling Motion",
  "title_text": "The Polynomially Self-repelling Motion",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bmd2qkath608q",
  "venue": "arXiv",
  "versions": []
}