{"paper":{"title":"Multivariate CLT follows from strong Rayleigh property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Robin Pemantle, Subhroshekhar Ghosh, Thomas M. Liggett","submitted_at":"2016-07-11T17:03:37Z","abstract_excerpt":"Let $(X_1 , \\ldots , X_d)$ be random variables taking nonnegative integer values and let $f(z_1, \\ldots , z_d)$ be the probability generating function. Suppose that $f$ is real stable; equivalently, suppose that the polarization of this probability distribution is strong Rayleigh. In specific examples, such as occupation counts of disjoint sets by a determinantal point process, it is known~\\cite{soshnikov02} that the joint distribution must approach a multivariate Gaussian distribution. We show that this conclusion follows already from stability of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03036","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":""},"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"}