{"paper":{"title":"A Central Limit Theorem for Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Felipe Gon\\c{c}alves","submitted_at":"2015-10-28T17:11:26Z","abstract_excerpt":"We prove an analogue of the Central Limit Theorem for operators. For every operator $K$ defined on $\\mathbb{C}[x]$ we construct a sequence of operators $K_N$ defined on $\\mathbb{C}[x_1,...,x_N]$ and demonstrate that, under certain orthogonality conditions, this sequence converges in a weak sense to an unique operator $\\mathcal{C}$. We show that this operator $\\mathcal{C}$ is a member of a family of operators $\\mathfrak{C}$ that we call {\\it Centered Gaussian Operators} and which coincides with the family of operators given by a centered Gaussian Kernel. Inspired in the approximation method use"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08381","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"}