{
  "abstract": "In this paper, we establish $p$-Wasserstein bounds and Cramér-type moderate deviations for the multi-dimensional elephant random walk in the diffusive and critical regimes. Using a Gaussian convolution estimate with random covariance and the recursions for the conditional covariance, we obtain $W_{p,2}(\\mathcal L(\\widehat T_n),N(0,I_d))\\le C_{a,d}pL_n$, where $\\widehat T_n$ is normalized by its exact covariance and \\[ L_n\\asymp \\begin{cases} n^{-1/2}\\log n,&a\\le1/3,\\\\ n^{-3(1/2-a)},&1/3<a<1/2,\\\\ (\\log n)^{-3/2},&a=1/2. \\end{cases} \\] Consequently, we obtain radial Cramér-type moderate deviations for $x=o(L_n^{-1/3})$. We also determine the covariance bias under the uncorrected normalization and establish the corresponding Wasserstein bounds, lower bounds and moderate deviation estimates. The dimension and the model parameters are fixed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01443",
  "author_total": 1,
  "authors": [
    {
      "name": "Shuyuan Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3g87z7pw5h1js.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01443",
  "fulltext_url": null,
  "id": "3g87z7pw5h1js",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01443",
  "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/2611.01443",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3g87z7pw5h1js.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01443",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01443"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "$p$-Wasserstein distance and Cramér-type moderate deviations for the multi-dimensional elephant random walk",
  "title_text": "p-Wasserstein distance and Cramér-type moderate deviations for the multi-dimensional elephant random walk",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3g87z7pw5h1js",
  "venue": "arXiv",
  "versions": []
}