{
  "abstract": "We prove quantitative sub-ballisticity for the self-avoiding walk on the lattice $\\mathbb{Z}^d$, $d\\geq 2$. Namely, we obtain an explicit exponential rate of decay for the probability that a self-avoiding walk of length $n$ reaches distance at least $vn$, in terms of $v>0$. As a consequence, we show that the displacement of an $n$-step self-avoiding walk is at most $n/\\exp(c\\log^* n)$ with very high probability. Previously, only a non-quantitative $o(n)$ bound was known from the work of Duminil-Copin and Hammond. Along the way, we show that at criticality the partition function of bridges of length $n$ is on average bounded by $C/\\log\\log n$, which we believe to be of independent interest. Our approach is based on a quantitative analysis of the original nonconstructive proof of Duminil-Copin and Hammond using ideas from proof theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40520",
  "author_total": 4,
  "authors": [
    {
      "name": "Ekin Arikök"
    },
    {
      "name": "Christoforos Panagiotis"
    },
    {
      "name": "Nicholas Pischke"
    },
    {
      "name": "Thomas Powell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ach1aefby3csz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40520",
  "fulltext_url": null,
  "id": "ach1aefby3csz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40520",
  "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.LO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ach1aefby3csz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quantitative sub-ballisticity of self-avoiding walk on $\\mathbb{Z}^d$",
  "title_text": "Quantitative sub-ballisticity of self-avoiding walk on ℤ^d",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/ach1aefby3csz",
  "venue": "arXiv",
  "versions": []
}