{
  "abstract": "Many mixing dynamical systems $(X,T,μ)$ are known to satisfy the hitting time statistics result \\[ \\lim_{r \\to 0} μ\\{\\, x : τ_{B(y,r)} (x) > t/μ(B(y,r))\\,\\} = e^{-t}, \\] for $μ$-almost every $y$, where $τ_{B(y,r)} (x)$ is the first hitting time of $x$ to the ball $B(y,r)$. Taking a different point of view, we fix $x$ and consider $τ_{B(y,r)} (x)$ as a function of $y$. We call this the visiting time of $y$ from $x$, i.e. the time it takes for $y$ to get a visit from $x$ within a neighbourhood of radius $r$. We prove that \\[ \\lim_{r \\to 0} μ\\{\\, y : τ_{B(y,r)} (x) > t/μ(B(y,r)) \\,\\} = e^{-t}, \\] for $μ$-almost every $x$. As a byproduct we obtain a new method of proof for hitting time statistics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01453",
  "author_total": 3,
  "authors": [
    {
      "name": "Maxim Kirsebom"
    },
    {
      "name": "Philipp Kunde"
    },
    {
      "name": "Tomas Persson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c92mbr286ert2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01453",
  "fulltext_url": null,
  "id": "c92mbr286ert2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01453",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7172436608",
  "pdf_url": "https://arxiv.org/pdf/2608.01453",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c92mbr286ert2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2608.01453",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01453"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Visiting time statistics",
  "title_text": "Visiting time statistics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/c92mbr286ert2",
  "venue": "arXiv",
  "versions": []
}