{"paper":{"title":"Second-order Poincar\\'e inequalities and localization on the Poisson space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. E. Yukich, Tara Trauthwein","submitted_at":"2026-05-22T07:05:41Z","abstract_excerpt":"Given a mean zero functional $F$ of a Poisson measure on a metric space, we apply the Malliavin-Stein method to establish sharpened second-order Poincar\\'e inequalities for $F/\\sqrt{\\operatorname{Var} (F)}$ in terms of fourth moments of difference operators. The rates of normal approximation are expressed in the Kolmogorov and Wasserstein distances and require fewer error terms than corresponding previous results. When $F$ is expressible as a sum of score functions which are distributionally close to scores having short-range structure, then we deduce that $F/\\sqrt{\\operatorname{Var}(F)}$ sati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23292","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/2605.23292/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"}