{
  "abstract": "We study upper tail large deviations for the first passage time in the frog model on $\\mathbb Z^d$, $d\\ge 2$. Let $\\mathrm{T}(0,x)$ denote the first time at which the infection, started from the origin, reaches $x$, and let $μ$ be the associated time constant. We prove that, for any Euclidean unit vector $v\\in\\mathbb R^d$ and $ξ>0$, \\[ \\lim_{n\\to\\infty} -\\frac{1}{\\mathfrak{s}_d(n)} \\log \\mathbb{P}\\bigl(\\mathrm{T}(0,\\lfloor nv\\rfloor) \\ge (μ(v)+ξ)n\\bigr) =\\mathfrak{r}_dξ, \\] where $\\mathfrak s_2(n)=n/\\log n$ and $\\mathfrak r_2=π$ for $d=2$; $\\mathfrak s_d(n)=n$ and $\\mathfrak r_d$ is the escape probability of simple random walk for $d\\ge3$. Moreover, on the upper tail large deviation event, we show that a certain slowdown mechanism occurs near the endpoint. To rule out other mechanisms, we analyze the growth of the infection near the starting point using a modified exploration process, and investigate its propagation through the intermediate region using the renormalization and covering arguments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14678",
  "author_total": 3,
  "authors": [
    {
      "name": "Van Hao Can"
    },
    {
      "name": "Naoki Kubota"
    },
    {
      "name": "Shuta Nakajima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5afgvx1mvy0t5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14678",
  "fulltext_url": null,
  "id": "5afgvx1mvy0t5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14678",
  "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": "W7221776840",
  "pdf_url": "https://arxiv.org/pdf/2610.14678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5afgvx1mvy0t5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Upper tail large deviation for the first passage time in the frog model on $Z^d$ with $d\\geq 2$",
  "title_text": "Upper tail large deviation for the first passage time in the frog model on Z^d with d≥ 2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/5afgvx1mvy0t5",
  "venue": "arXiv",
  "versions": []
}