{"paper":{"title":"Scaling limits of discrete copulas are bridged Brownian sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Carlos Tomei, Juliana Freire, Nicolau C. Saldanha","submitted_at":"2016-01-13T17:26:53Z","abstract_excerpt":"For large $n$, take a random $n \\times n$ permutation matrix and its associated discrete copula $X_n$. For $a, b = 0, 1, \\ldots, n$, let $y_n(\\frac{a}{n},\\frac{b}{n}) = \\frac{1}{n} ( X_{a,b} - \\frac{ab}{n} )$; define $y_n: [0,1]^2 \\to R$ by interpolating quadratically on squares of side $\\frac{1}{n}$. We prove a Donsker type central limit theorem: $\\sqrt{n} y_n$ approaches a bridged Brownian sheet on the unit square."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03321","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"}