{"paper":{"title":"Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Parthanil Roy, Stilian A. Stoev, Yizao Wang","submitted_at":"2009-11-03T18:34:22Z","abstract_excerpt":"We establish characterization results for the ergodicity of stationary symmetric $\\alpha$-stable (S$\\alpha$S) and $\\alpha$-Frechet random fields. We show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803] remains valid in the multiparameter setting, that is, a stationary S$\\alpha$S ($0<\\alpha<2$) random field is ergodic (or, equivalently, weakly mixing) if and only if it is generated by a null group action. Similar results are also established for max-stable random fields. The key ingredient is the adaption of a characterization of positive/null recurrence of group actions by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0610","kind":"arxiv","version":3},"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"}