{"paper":{"title":"Maximum of a log-correlated Gaussian field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Thomas Madaule","submitted_at":"2013-07-04T15:08:52Z","abstract_excerpt":"We study the maximum of a Gaussian field on $[0,1]^\\d$ ($\\d \\geq 1$) whose correlations decay logarithmically with the distance. Kahane \\cite{Kah85} introduced this model to construct mathematically the Gaussian multiplicative chaos in the subcritical case. Duplantier, Rhodes, Sheffield and Vargas \\cite{DRSV12a} \\cite{DRSV12b} extended Kahane's construction to the critical case and established the KPZ formula at criticality. Moreover, they made in \\cite{DRSV12a} several conjectures on the supercritical case and on the maximum of this Gaussian field. In this paper we resolve Conjecture 12 in \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1365","kind":"arxiv","version":3},"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"}