{"paper":{"title":"Four-moment criteria for Poisson convergence on Poisson and Rademacher chaoses","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangqu Zheng","submitted_at":"2026-08-12T17:54:07Z","abstract_excerpt":"In this paper, we establish Poisson limit theorems on Poisson and Rademacher chaoses. Our principal result is a total-variation bound, valid in both settings, for an integer-valued functional whose highest-order chaos is dominant. The approximation error is the sum of the pure-chaos four-moment terms and an explicit remainder controlled by the $L^4$-size of the lower-order chaoses. On Poisson space the pure-chaos term is controlled solely by the moment defect, whereas on Rademacher space an additional maximal-influence correction is required. When the lower-order remainder vanishes, we recover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12451","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.12451/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}