{"paper":{"title":"Strong mixing properties of max-infinitely divisible random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cl\\'ement Dombry (LMA), Fr\\'ed\\'eric Eyi-Minko (LMA)","submitted_at":"2012-01-23T08:23:17Z","abstract_excerpt":"Let $\\eta=(\\eta(t))_{t\\in T}$ be a sample continuous max-infinitely random field on a locally compact metric space $T$. For a closed subset $S\\in T$, we note $\\eta_{S}$ the restriction of $\\eta$ to $S$. We consider $\\beta(S_1,S_2)$ the absolute regularity coefficient between $\\eta_{S_1}$ and $\\eta_{S_2}$, where $S_1,S_2$ are two disjoint closed subsets of $T$. Our main result is a simple upper bound for $\\beta(S_1,S_2)$ involving the exponent measure $\\mu$ of $\\eta$: we prove that $\\beta(S_1,S_2)\\leq 2\\int \\bbP[\\eta\\not<_{S_1} f,\\ \\eta\\not <_{S_2} f]\\,\\mu(df)$, where $f\\not<_{S} g$ means that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4645","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"}