{
  "abstract": "We consider Brownian last passage percolation (BLPP) in which the Brownian increment process on each unit horizontal interval is independently resampled at rate one. By combining strong passage-time stability estimates with a multiscale analysis of static near-optimal paths, we show that, for every $\\varepsilon>0$, the union of all geodesics between two KPZ-scale rectangles of transverse width of order $n^{2/3}$ and longitudinal length of order $n$, separated by a distance of order $n$, visits at most $n^{1+\\varepsilon}$ unit horizontal cells in the bulk during the critical time interval $[0,n^{-1/3}]$, both in expectation and with stretched-exponentially high probability. We also obtain the quantitative bound $n\\exp\\{C(\\log\\log n)^2\\}$ on the expected hitset size, with a corresponding failure probability at most $Ce^{-c(\\log n)^2}$. Using this, we establish that the set of times admitting a non-trivial bigeodesic has almost surely zero Hausdorff measure for the subpolynomially decaying gauge $H(r)=\\exp\\{-L(r)^2\\log L(r)\\}$, where $L(r)=\\log\\log(1/r)$, as $r\\downarrow0$. In particular, this set almost surely has Hausdorff dimension zero. For each fixed deterministic non-axial direction, we further show that almost surely no time admits a bigeodesic in that direction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35103",
  "author_total": 1,
  "authors": [
    {
      "name": "Manan Bhatia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a7pb4xdamsnw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35103",
  "fulltext_url": null,
  "id": "9a7pb4xdamsnw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35103",
  "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": "W7214771006",
  "pdf_url": "https://arxiv.org/pdf/2609.35103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9a7pb4xdamsnw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Geodesic traces in dynamical Brownian last passage percolation",
  "title_text": "Geodesic traces in dynamical Brownian last passage percolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/9a7pb4xdamsnw",
  "venue": "arXiv",
  "versions": []
}