{
  "abstract": "We study boundary transmission and excursion geometry in the planar Lorentz mirror model through finite-volume numerical experiments. Cylinder penetration quantiles grow approximately linearly with circumference over the simulated range, with a systematic upward drift in the normalized quantiles when vacancies are present. Estimated slab-transmission probabilities yield exponential confinement bounds with quantified statistical confidence at the tested widths. Planar excursions conditioned to reach a distant boundary exhibit transverse ranges proportional to the exit radius, while their repeated-visit fractions vary strongly with mirror density. Endpoint-label collision probabilities substantially exceed a general gluing lower bound, although they account for only part of the observed same-column crossing probability. Finally, rerouting at repeated vertices preserves the exit while substantially shortening the sampled paths. These findings characterize finite-volume transport and excursion geometry without determining an asymptotic scaling exponent or resolving infinite-plane localization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14949",
  "author_total": 2,
  "authors": [
    {
      "name": "Jian Gu"
    },
    {
      "name": "Qin Hao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4t8d5mbja1tk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14949",
  "fulltext_url": null,
  "id": "b4t8d5mbja1tk",
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  "landing_url": "https://arxiv.org/abs/2609.14949",
  "language": null,
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  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math-ph"
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      "arxiv",
      "math.MP"
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      "arxiv",
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7213258924",
  "pdf_url": "https://arxiv.org/pdf/2609.14949",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4t8d5mbja1tk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14949",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14949"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Boundary transmission and excursion geometry in the Lorentz mirror model: a numerical study",
  "title_text": "Boundary transmission and excursion geometry in the Lorentz mirror model: a numerical study",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/b4t8d5mbja1tk",
  "venue": "arXiv",
  "versions": []
}