{"paper":{"title":"Maximum of the Ginzburg-Landau fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"David Belius, Wei Wu","submitted_at":"2016-10-13T18:36:58Z","abstract_excerpt":"We study two dimensional massless field in a box with potential $V\\left( \\nabla \\phi \\left( \\cdot \\right) \\right) $ and zero boundary condition, where $V$ is any symmetric and uniformly convex function. Naddaf-Spencer and Miller proved the macroscopic averages of this field converge to a continuum Gaussian free field. In this paper we prove the distribution of local marginal $\\phi \\left( x\\right) $, for any $x$ in the bulk, has a Gaussian tail. We further characterize the leading order of the maximum and dimension of high points of this field, thus generalize the results of Bolthausen-Deuschel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04195","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":""},"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"}