{"paper":{"title":"Moderate Deviations for Gaussian Maxima and an Entropy Proof of Critical SK Free Energy Fluctuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yiming Chen","submitted_at":"2026-07-23T14:55:06Z","abstract_excerpt":"We study two problems for Gaussian maxima. First, let $(X_1,\\ldots,X_N)$ be a centered Gaussian vector with $\\operatorname{Var}(X_i)\\leq 1$. If, for fixed $\\alpha\\in(0,\\sqrt{2})$ and $\\kappa>0$, one has $\\mathbb{E}\\max_i X_i\\geq\\alpha\\sqrt{\\log N}$ and $\\mathbb{E}\\max_i X_i+\\kappa\\sqrt{\\log N}\\leq\\sqrt{2\\log N}$, then \\[ \\mathbb{P}\\left(\\max_i X_i\\geq \\mathbb{E}\\max_i X_i+\\kappa\\sqrt{\\log N}\\right) \\leq N^{-\\kappa^2/(2-\\alpha^2)+o(1)}. \\] This answers a question of Ding, Eldan and Zhai, and the exponent is attained by an equicorrelated Gaussian field. Second, for the Sherrington--Kirkpatrick m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21392","kind":"arxiv","version":1},"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/2607.21392/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"}