{
  "abstract": "We study the two-dimensional directed polymer model in a Gaussian environment which is independent in time and spatially correlated, with covariances h(x) either summable or with a critical decay, satisfying h(x)∼(log|x|)a/|x|2 as |x|→∞ for some a>−1. We determine the precise high-temperature asymptotics of the free energy, confirming a conjecture of Lacoin (Ann. Probab. 2011), later refined by Cosco, Cottini and Donadini (2025). We also establish a phase transition for the diffusively rescaled partition functions: below some critical point they converge to the Lebesgue measure, while above it they converge to zero. A key feature of our approach is that both results are obtained using only second-moment estimates and are based on a simplified change-of-measure argument in the supercritical regime, that may prove useful for other disordered models.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30829",
  "author_total": 2,
  "authors": [
    {
      "name": "Quentin Berger"
    },
    {
      "name": "Francesca Cottini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01xzsbebcj4aq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30829",
  "fulltext_url": null,
  "id": "01xzsbebcj4aq",
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  "landing_url": "https://hal.science/hal-05736323v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math.PR"
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7204956530",
  "pdf_url": "https://hal.science/hal-05736323/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01xzsbebcj4aq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05736323",
      "source": "hal",
      "url": "https://hal.science/hal-05736323v1"
    },
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2608.30829",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30829"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Free energy and phase transition for 2D directed polymers with critical spatial correlations",
  "title_text": "Free energy and phase transition for 2D directed polymers with critical spatial correlations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/01xzsbebcj4aq",
  "venue": "HAL",
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}