{"paper":{"title":"Extremes of homogeneous Gaussian random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof D\\k{e}bicki, Natalia Soja-Kukie{\\l}a","submitted_at":"2013-12-10T16:37:02Z","abstract_excerpt":"Let $\\{X(s,t):s,t\\geqslant 0\\}$ be a centered homogeneous Gaussian field with a.s. continuous sample paths and correlation function $r(s,t)=Cov(X(s,t),X(0,0))$ such that \\[r(s,t)=1-|s|^{\\alpha_1}-|t|^{\\alpha_2}+o(|s|^{\\alpha_1}+|t|^{\\alpha_2}), \\quad s,t \\to 0,\\] with $\\alpha_1,\\alpha_2\\in(0,2],$ and $r(s,t)<1$ for $(s,t)\\neq(0,0)$. In this contribution we derive an exact asymptotic expansion (as $u\\to \\infty$) of $$\\mathbb{P}\\left(\\sup_{(s n_1(u),t n_2(u))\\in\\left[0,x\\right]\\times\\left[0,y\\right]}X(s,t)\\leqslant u\\right),$$ where $n_1(u)n_2(u)=u^{2/\\alpha_1+2/\\alpha_2}\\Psi(u)$, which holds un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2863","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"}