{
  "abstract": "We establish an identity relating the spatial derivative of a two-point free-energy correlation to two fundamental geometric quantities: the annealed probability that two independently sampled polymers, in the same environment, meet before reaching the prescribed terminal level, and the exit-point location of a single polymer. Our result is inspired in part by recent integration-by-parts work of Gu and Quastel for the KPZ equation. A crucial step in their continuous setting relies on an ingenious application of Itô's formula, which has no direct analogue in our semi-discrete setting. Instead, we exploit intrinsic symmetries of the polymer model together with the memoryless property. We also provide two applications: (i) we recover the horizontal Burke property by proving that the anchored stationary horizontal free-energy profile is a two-sided Brownian motion; (ii) in the zero-temperature limit, we obtain the corresponding identity for Brownian last-passage percolation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02064",
  "author_total": 4,
  "authors": [
    {
      "name": "Firas Rassoul-Agha"
    },
    {
      "name": "Xiao Shen"
    },
    {
      "name": "Ruixuan Zhang"
    },
    {
      "name": "Guangqu Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1phcr1v9rnkyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02064",
  "fulltext_url": null,
  "id": "1phcr1v9rnkyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02064",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7207848176",
  "pdf_url": "https://arxiv.org/pdf/2609.02064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1phcr1v9rnkyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Coalescence and fluctuations of O'Connell$\\unicode{x2013}$Yor polymers via the free-energy correlation profile",
  "title_text": "Coalescence and fluctuations of O'Connellunicodex2013Yor polymers via the free-energy correlation profile",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/1phcr1v9rnkyk",
  "venue": "arXiv",
  "versions": []
}