{"paper":{"title":"Extremes of multidimensional stationary Gaussian random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Natalia Soja-Kukie{\\l}a","submitted_at":"2016-10-10T12:40:32Z","abstract_excerpt":"Let $\\{X(\\mathbf{t}):\\mathbf{t}=(t_1, t_2, \\ldots, t_d)\\in[0,\\infty)^d\\}$ be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function $r$ satisfying conditions $r(\\mathbf{t})<1$ for every $\\mathbf{t}\\neq \\mathbf{0}$ and $r(\\mathbf{t})=1-\\sum_{i=1}^d |t_i|^{\\alpha_i} + o(\\sum_{i=1}^d |t_i|^{\\alpha_i})$, as $\\mathbf{t}\\to\\mathbf{0}$, with constants $\\alpha_1, \\alpha_2, \\ldots, \\alpha_d \\in(0,2]$. The main result of this contribution is the description of the asymptotic behaviour of $P(\\sup\\{X(\\mathbf{t}): \\mathbf{t}\\in\\mathcal{J}^{\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02888","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"}