{"paper":{"title":"$q$-Chaos","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Hun Hee Lee, Marius Junge","submitted_at":"2008-01-24T05:23:11Z","abstract_excerpt":"We consider the $L_p$ norm estimates for homogeneous polynomials of $q$-gaussian variables ($-1\\leq q\\leq 1$). When $-1<q<1$ the $L_p$ estimates for $1\\leq p \\leq 2$ are essentially the same as the free case ($q=0$), whilst the $L_p$ estimates for $2\\leq p \\leq \\infty$ show a strong $q$-dependence. Moreover, the extremal cases $q = \\pm 1$ produce decisively different formulae."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3704","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/0801.3704/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"}