{
  "abstract": "For any $t\\in [0,1/2)$, consider the process $η_t:[0,1/2]\\mapsto\\mathbb{R}$ defined by $η_t(s)=Π(t+s)-Π(t)$, where $Π$ is the directed geodesic from $(0,0)$ to $(0,1)$ in the directed landscape. Let $0\\leq t<u<1/2$. We show that the laws of $η_t$ and $η_u$ are mutually absolutely continuous if and only if $t>0$. This proves Conjecture 14.5 in Dauvergne, Ortmann, and Virág, 2022 in the affirmative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39675",
  "author_total": 2,
  "authors": [
    {
      "name": "Pantelis Tassopoulos"
    },
    {
      "name": "Sourav Sarkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dyhv75b8jyzj5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39675",
  "fulltext_url": null,
  "id": "dyhv75b8jyzj5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39675",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7215109626",
  "pdf_url": "https://arxiv.org/pdf/2609.39675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dyhv75b8jyzj5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The starting point of a directed geodesic is special",
  "title_text": "The starting point of a directed geodesic is special",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/dyhv75b8jyzj5",
  "venue": "arXiv",
  "versions": []
}