{
  "abstract": "Random-walk loop-catchers (RWLC) are a one-parameter family of random subsets of the trace of a random walk, recently introduced in [Cai 2026, arXiv:2607.18070], which interpolates between loop-erased random walk (LERW) and the full walk trace, satisfying a recovery property. We prove that the continuous version of this recovery property uniquely characterizes the scaling limit of LERW and RWLC in three dimensions, using a Green-function test via entangled multipath LERW, as outlined in [Cai 2026, arXiv:2607.18070]. For LERW, this resolves the 3D case of the conjecture of Sapozhnikov--Shiraishi [Sapozhnikov--Shiraishi 2018, Probab. Theory Related Fields 172, 615--662] and gives a new and axiomatic proof of the existence of the scaling limit, which was first proved in [Kozma 2007, Acta Math. 199, 29--152]. For RWLC, this gives the construction of 3D Brownian loop-catchers. The characterization also yields inversion invariance of the 3D LERW scaling limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12047",
  "author_total": 3,
  "authors": [
    {
      "name": "Gefei Cai"
    },
    {
      "name": "Xinyi Li"
    },
    {
      "name": "Daisuke Shiraishi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06fn7h7ycqfst.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12047",
  "fulltext_url": null,
  "id": "06fn7h7ycqfst",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12047",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7221163089",
  "pdf_url": "https://arxiv.org/pdf/2610.12047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06fn7h7ycqfst.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Characterization and scaling limit of three-dimensional loop-erased random walk and random-walk loop-catchers",
  "title_text": "Characterization and scaling limit of three-dimensional loop-erased random walk and random-walk loop-catchers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/06fn7h7ycqfst",
  "venue": "arXiv",
  "versions": []
}