{"paper":{"title":"Extrema of locally stationary Gaussian fields on growing manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Wanli Qiao, Wolfgang Polonik","submitted_at":"2015-10-23T05:23:57Z","abstract_excerpt":"We consider a class of non-homogeneous, continuous, centered Gaussian random fields $\\{X_h(t), t \\in {\\cal M}_h;\\,0 < h \\le 1\\}$ where ${\\cal M}_h$ denotes a rescaled smooth manifold, i.e. ${\\cal M}_h = \\frac{1}{h} {\\cal M},$ and study the limit behavior of the extreme values of these Gaussian random fields when $h$ tends to zero, which means that the manifold is growing. Our main result can be thought of as a generalization of a classical result of Bickel and Rosenblatt (1973a), and also of results by Mikhaleva and Piterbarg (1997)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06833","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"}