{
  "abstract": "We determine the exact first-order asymptotics of the expected optimal cost in two-dimensional random bipartite matching, for every finite power cost $q \\ge 1$, on the flat torus. In the endpoint case $q=1$, this answers a question by Talagrand, in the periodic case. The argument involves the closely related asymptotics of the energy of the solution of the $p$-Poisson equation with a regularized white-noise source. In the limit of vanishing regularization parameter, we identify this energy as the solution of a Variational Martingale Problem on a limiting Gaussian filtration, whose value is characterized by a parabolic Monge-Ampère flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08717",
  "author_total": 4,
  "authors": [
    {
      "name": "Victor Armegioiu"
    },
    {
      "name": "Michael Goldman"
    },
    {
      "name": "Francesco Grotto"
    },
    {
      "name": "Dario Trevisan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwaa777dh4fd9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08717",
  "fulltext_url": null,
  "id": "cwaa777dh4fd9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08717",
  "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.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212062378",
  "pdf_url": "https://arxiv.org/pdf/2609.08717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwaa777dh4fd9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.08717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exact Asymptotics for the 2D Euclidean Random Matching Problem",
  "title_text": "Exact Asymptotics for the 2D Euclidean Random Matching Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/cwaa777dh4fd9",
  "venue": "arXiv",
  "versions": []
}