{
  "abstract": "We study a rate-one Poissonization of the one-dimensional elephant random walk killed upon reaching $\\pm N$. For every fixed memory parameter $0<p<1$, we give a self-contained proof of two-sided exponential survival bounds on the rate scale $N^{-2}$, uniformly for sufficiently large $N$ and times $t\\ge TN^3$. Our approach combines the classical Dirichlet Poincaré inequality with an $O(N/t)$ estimate on the memory-dependent perturbation and a quantitative initialization of the principal-eigenvector projection. The lower bound covers the critical and superdiffusive regimes $3/4\\le p<1$ in this late-time range. The confined-path comparison used for initialization also gives a direct proof of the lower bound. The spectral argument controls the exponentially small forcing terms and jumps introduced by Poisson truncation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.08884",
  "author_total": 3,
  "authors": [
    {
      "name": "Cristian Favio Coletti"
    },
    {
      "name": "Rafael de Mattos Grisi"
    },
    {
      "name": "Ioannis Papageorgiou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/239wh0627g3en.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.08884",
  "fulltext_url": null,
  "id": "239wh0627g3en",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.08884",
  "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": "W7163992972",
  "pdf_url": "https://arxiv.org/pdf/2606.08884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/239wh0627g3en.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2606.08884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.08884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Spectral Approach to Survival Bounds for the Elephant Random Walk",
  "title_text": "A Spectral Approach to Survival Bounds for the Elephant Random Walk",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/239wh0627g3en",
  "venue": "arXiv",
  "versions": []
}