{
  "abstract": "In directed last-passage percolation with i.i.d. exponential vertex weights, the coalescence time $\\operatorname{Coal}(a,b)$ of two semi-infinite geodesics started from vertices $a$ and $b$ in a fixed direction has a heavy tail with (KPZ) exponent $2/3$, and hence infinite expectation. We study instead the first coalescence among triples of semi-infinite geodesics in first- and last-passage percolation models (FPP/LPP) on $\\mathbb{Z}^2$ that arise from stationary compatible families, such as Busemann geodesics. For directed FPP and LPP with arbitrary weights, we prove that $$\\mathbb{E}\\bigl[\\min\\{\\operatorname{Coal}(a,a-e_1),\\operatorname{Coal}(a,a-e_2)\\}\\bigr]<\\infty.$$ We also consider FPP and LPP models in which antidiagonal motion is allowed, and prove that for every integer $k>0$, \\[\\mathbb{E}\\bigl[\\min\\{\\operatorname{Coal}(a,a-k(e_1-e_2)),\\operatorname{Coal}(a,a+k(e_1-e_2))\\}\\bigr]<\\infty.\\] These results support the heuristic prediction that adjacent coalescence times are negatively associated.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27433",
  "author_total": 3,
  "authors": [
    {
      "name": "Arjun Krishnan"
    },
    {
      "name": "Firas Rassoul-Agha"
    },
    {
      "name": "Timo Seppäläinen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c5q71yb9ynt94.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27433",
  "fulltext_url": null,
  "id": "c5q71yb9ynt94",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27433",
  "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": "W7223120604",
  "pdf_url": "https://arxiv.org/pdf/2610.27433",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c5q71yb9ynt94.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27433",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27433"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "First pair coalescence among three geodesics",
  "title_text": "First pair coalescence among three geodesics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/c5q71yb9ynt94",
  "venue": "arXiv",
  "versions": []
}