{"paper":{"title":"An exceptional max-stable process fully parameterized by its extremal coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Kirstin Strokorb, Martin Schlather","submitted_at":"2015-04-14T08:56:45Z","abstract_excerpt":"The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\\subset T$ the effective number of independent random variables among the collection $\\{X_t\\}_{t\\in A}$. We introduce the class of Tawn-Molchanov processes that is in a 1:1 correspondence with the class of ECFs, thus also proving a complete characterization of the ECF in terms of negative definiteness. The corresponding Tawn-Molchanov process turns out to be exceptional among all max-stable processes sharing the same ECF in that its dependency set is maximal w.r.t. inclusio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03459","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"}