{"paper":{"title":"On the rate of convergence in de Finetti's representation theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Giovanni Peccati, Guillaume Mijoule, Yvik Swan","submitted_at":"2016-01-25T14:01:18Z","abstract_excerpt":"A consequence of de Finetti's representation theorem is that for every infinite sequence of exchangeable 0-1 random variables $(X_k)_{k\\geq1}$, there exists a probability measure $\\mu$ on the Borel sets of $[0,1]$ such that $\\bar X_n = n^{-1} \\sum_{i=1}^n X_i$ converges weakly to $\\mu$. For a wide class of probability measures $\\mu$ having smooth density on $(0,1)$, we give bounds of order $1/n$ with explicit constants for the Wasserstein distance between the law of $\\bar X_n$ and $\\mu$. This extends a recent result {by} Goldstein and Reinert \\cite{goldstein2013stein} regarding the distance be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06606","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"}