{"paper":{"title":"Extremes of Gaussian fields with a product term in the variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Svyatoslav Novikov","submitted_at":"2026-05-21T17:24:12Z","abstract_excerpt":"We study the high excursion probability of a centered Gaussian field on a square.\n  Writing \\(\\sigma\\) and \\(r\\) for its standard deviation and correlation function,\n  we assume that \\(\\sigma\\) has a unique maximum at the corner\n  \\(\\boldsymbol{0}=(0,0)\\) and\n  \\[\n  1-\\sigma(\\boldsymbol{t}) \\sim t_1^\\beta+t_2^\\beta+t_1^a t_2^a ,\n  \\qquad \\boldsymbol{t}=(t_1,t_2)\\to\\boldsymbol{0}\n  \\]\n  in \\(\\mathbb R_+^2\\). The local correlation is assumed to satisfy\n  \\[\n  1-r(\\boldsymbol{t},\\boldsymbol{s})\\sim |t_1-s_1|^\\alpha+|t_2-s_2|^\\alpha,\n  \\qquad 0<\\alpha<\\beta .\n  \\]\n  This product form of the standa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22760","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/2605.22760/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"}