{
  "abstract": "Motivated by the study of the level lines of the $(2+1)$D Solid-On-Solid (SOS) model above a floor, near the corners of the box, we derive the limit law of an ensemble of $K$ curves from a $(1+1)$D SOS model, with an area tilt, and above a wedge-shaped floor in $\\{-N,\\ldots,N\\}$. We show that there exist explicit critical points $α_0=1>α_1>\\ldots>α_K>0$ such that, for each $r \\geq 1$, along the intervals $\\pm(α_{r} N,α_{r-1} N)$, the bottom $K+1-r$ curves, rescaled by $(N^{2/3},N^{1/3})$, tend to the law of a Geometrically-Area-Tilted Ensemble of non-crossing Brownian paths (Brownian GATE), independently across those $2K$ intervals. All other curves, centered and rescaled by $(N,\\sqrt{N})$, tend to a product of $K$ suitable Brownian bridges.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.05262",
  "author_total": 3,
  "authors": [
    {
      "name": "Amir Dembo"
    },
    {
      "name": "Eyal Lubetzky"
    },
    {
      "name": "Ofer Zeitouni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24kwxwkc5je4g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.05262",
  "fulltext_url": null,
  "id": "24kwxwkc5je4g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.05262",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7201869437",
  "pdf_url": "https://arxiv.org/pdf/2608.05262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24kwxwkc5je4g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2608.05262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.05262"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The law of (1+1)D SOS with an area tilt in a wedge",
  "title_text": "The law of (1+1)D SOS with an area tilt in a wedge",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/24kwxwkc5je4g",
  "venue": "arXiv",
  "versions": []
}