{
  "abstract": "Let $Z_N^{β_N}(x)$ denote the partition function of the two-dimensional directed polymer started at $x\\in \\mathbb{Z}^2$, in Gaussian environemnt, in the critical window, with parameter $β_N=\\sqrt{(1-\\vartheta/\\log N)/R_N}$. Here $R_N\\sim (\\log N)/π$ is the truncated collision Green function at the origin for the simple random walk on $\\mathbb{Z}^2$. Let $\\mathfrak M_N$ denote the maximum of $\\log Z_N(x)$ over $|x|_\\infty\\leq \\sqrt{N}$. We prove that, for any $\\vartheta\\in \\mathbb{R}$, in probability, $$\\mathfrak M_N/\\sqrt{\\log N}\\to 2\\sqrt{2}\\text{ as }N\\to\\infty.$$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41989",
  "author_total": 3,
  "authors": [
    {
      "name": "Clement Cosco"
    },
    {
      "name": "Shuta Nakajima"
    },
    {
      "name": "Ofer Zeitouni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxfbzg7f8xkg2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41989",
  "fulltext_url": null,
  "id": "cxfbzg7f8xkg2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41989",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxfbzg7f8xkg2.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41989"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Maximum of the Two-Dimensional Directed Polymer in the Critical Window",
  "title_text": "Maximum of the Two-Dimensional Directed Polymer in the Critical Window",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/cxfbzg7f8xkg2",
  "venue": "arXiv",
  "versions": []
}