{"paper":{"title":"Extremes of Gaussian Random Fields with regularly varying dependence structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzyztof D\\k{e}bicki, Peng Liu","submitted_at":"2016-05-28T23:12:37Z","abstract_excerpt":"Let $X(t), t\\in \\mathcal{T}$ be a centered Gaussian random field with variance function $\\sigma^2(\\cdot)$ that attains its maximum at the unique point $t_0\\in \\mathcal{T}$, and let $M(\\mathcal{T}):=\\sup_{t\\in \\mathcal{T}} X(t)$. For $\\mathcal{T}$ a compact subset of $\\R$, the current literature explains the asymptotic tail behaviour of $M(\\mathcal{T})$ under some regularity conditions including that $1- \\sigma(t)$ has a polynomial decrease to 0 as $t \\to t_0$. In this contribution we consider more general case that $1- \\sigma(t)$ is regularly varying at $t_0$. We extend our analysis to random "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08946","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"}