{"paper":{"title":"A limit law for the maximum of subcritical DG-model on a hierarchical lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Haiyu Huang, Marek Biskup","submitted_at":"2023-09-17T22:21:05Z","abstract_excerpt":"We study the extremal properties of the \"integer-valued Gaussian\" a.k.a.\\ DG-model on the hierarchical lattice $\\Lambda_n:=\\{1,\\dots,b\\}^n$ (with $b\\ge2$) of depth $n$. This is a random field $\\varphi\\in\\mathbb Z^{\\Lambda_n}$ with law proportional to $e^{\\frac12\\beta(\\varphi,\\Delta_n\\varphi)}\\prod_{x\\in\\Lambda_n}\\#(d\\varphi_x)$, where $\\Delta_n$ is the hierarchical Laplacian, $\\beta$ is the inverse temperature and $\\#$ is the counting measure on $\\mathbb Z$. Denoting $\\beta_c:=2\\pi^2/\\log b$ and $m_n:=\\beta^{-1/2}[(2\\log b)^{1/2}n-\\frac32(2\\log b)^{-1/2}\\log n]$, for $0<\\beta<\\beta_c$ we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09389","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.09389/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}