{"paper":{"title":"The tail of the maximum of smooth Gaussian fields on fractal sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Marc Aza\\\"is, Mario Wschebor","submitted_at":"2011-09-18T17:55:01Z","abstract_excerpt":"We study the probability distribution of the maximum $M_S $ of a smooth stationary Gaussian field defined on a fractal subset $S$ of $\\R^n$. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution $\\P(M_S>u)$ as $u\\rightarrow +\\infty.$ The basic tool is Rice formula for the moments of the number of local maxima of a random field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3895","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":""},"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"}