{
  "abstract": "In this paper, we study the effect of an external random field on the localisation / delocalisation of the long-range Discrete Gaussian Chain (DGC), recently studied by Garban arXiv:2312.04536 and Coquille \\emph{et al.} arXiv:2412.15782. We prove that the model is delocalised at every inverse temperature for any polynomial decay $α> 3/2$. This behaviour differs qualitatively from the one of the disorder-free long-range DGC, for which delocalisation at every temperature occurs only for $α> 2$, similarly to what happens for long-range Ising models as already proved by Aizenman and Wehr. Additionally, we provide a more detailed description of the delocalised phase by identifying the growth exponent and scaling limit of the height at the origin for any decay exponent $α> 3/2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18786",
  "author_total": 4,
  "authors": [
    {
      "name": "Christopher Chalhoub"
    },
    {
      "name": "Paul Dario"
    },
    {
      "name": "Corentin Faipeur"
    },
    {
      "name": "Arnaud Le Ny"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7cdejhyqj457s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18786",
  "fulltext_url": null,
  "id": "7cdejhyqj457s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18786",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213522378",
  "pdf_url": "https://arxiv.org/pdf/2609.18786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7cdejhyqj457s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain",
  "title_text": "Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/7cdejhyqj457s",
  "venue": "arXiv",
  "versions": []
}