{"paper":{"title":"Scaling limits for random fields with long-range dependence","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ilkka Norros, Ingemar Kaj, Lasse Leskel\\\"a, Volker Schmidt","submitted_at":"2007-07-25T12:52:42Z","abstract_excerpt":"This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $\\lambda$ of the sets grows to infinity and the mean volume $\\rho$ of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show that the centered and renormalized random field can have three different limits, depending on the relative speed at which $\\lambda$ and $\\rho$ are scaled. If $\\lambda$ grows much faster than $\\rho$ shrinks, the limit is Gaussian with long-range dependence, while in the opposite case, the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3729","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"}