{
  "abstract": "We prove precise large deviations for the symmetric elephant random walk with random step sizes. When the distribution of $|Z_1-1|$ is subexponential, we first show that, for each fixed$p\\in[0,1]$, there exists a positive number sequence $b_n\\to\\infty$ such that \\[ \\mathbb P(S_n>x)\\sim \\mathbb P(S_n<-x)\\sim \\frac n2\\overline F(x) \\] uniformly for $x\\ge b_n$, where $\\overline F(x)=\\mathbb P(|Z_1-1|>x)$. This existence result requires no moment assumptions and does not specify the growth rate of $b_n$. For $p\\in[0,3/4]$, we further give explicit sufficient conditions on $b_n$ under Weibull-type and lognormal-type tail conditions with a regularly varying factor $x^γL(x)$, where $γ\\in\\mathbf R$ and $L$ is a positive measurable slowly varying function. Analogous results hold with $\\mathbb P(|Z_1|>x)$ and non-strict tails.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01440",
  "author_total": 1,
  "authors": [
    {
      "name": "Shuyuan Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffspc2cne6gsj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01440",
  "fulltext_url": null,
  "id": "ffspc2cne6gsj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01440",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01440",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffspc2cne6gsj.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01440",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01440"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Precise large deviations for the elephant random walk with Weibull-type and lognormal-type random step sizes",
  "title_text": "Precise large deviations for the elephant random walk with Weibull-type and lognormal-type random step sizes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ffspc2cne6gsj",
  "venue": "arXiv",
  "versions": []
}