{"paper":{"title":"New moments criteria for convergence towards normal product/tetilla laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dario Gasbarra, Ehsan Azmoodeh","submitted_at":"2017-08-25T10:29:10Z","abstract_excerpt":"In the framework of classical probability, we consider the normal product distribution $F_\\infty \\sim N_1 \\times N_2$ where $N_1, N_2$ are two independent standard normal random variable, and in the setting of free probability, $F_\\infty \\sim \\left( S_1 S_2 + S_2 S_1 \\right)/\\sqrt{2}$ known as {\\it tetilla law} \\cite{d-n}, where $S_1, S_2$ are freely independent normalized semicircular random variables. We provide novel characterization of $F_\\infty$ within the second Wiener (Wigner) chaos. More precisely, we show that for any generic element $F$ in the second Wiener (Wigner) chaos with varian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07681","kind":"arxiv","version":2},"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"}