{
  "abstract": "We study the one-dimensional elephant random walk with two memory channels introduced by Saha [Phys.\\ Rev.\\ E \\textbf{106}, L062105 (2022)] with memory parameter $p\\in(0,1)$. Maulik, Roy and Sadhukhan [arXiv:2509.10225] proved recurrence for $p\\le11/16$ and transience for $p>7/8$, leaving the range $11/16<p\\le7/8$ open. We close this gap by proving that $p=11/16$ is the exact recurrence--transience threshold and by determining how fast the walk escapes from the origin throughout the transient regime. For $11/16<p<7/8$, we also show that the scaling limit obtained by Maulik, Roy and Sadhukhan is almost surely nonzero. At $p=7/8$, we prove that the walk is transient with zero asymptotic velocity and escapes at the scale $n/\\sqrt{\\log n}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06641",
  "author_total": 1,
  "authors": [
    {
      "name": "Ngo Phuoc Nguyen Ngoc"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahcefpd9vg1ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06641",
  "fulltext_url": null,
  "id": "ahcefpd9vg1ca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06641",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212054093",
  "pdf_url": "https://arxiv.org/pdf/2609.06641",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahcefpd9vg1ca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06641",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06641"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Recurrence, Transience, and the Rate of Escape for Elephant Random Walks with Two Memory Channels",
  "title_text": "Recurrence, Transience, and the Rate of Escape for Elephant Random Walks with Two Memory Channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/ahcefpd9vg1ca",
  "venue": "arXiv",
  "versions": []
}