{"paper":{"title":"Distribution functions, extremal limits and optimal transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Maria Rita Iac\\`o, Robert F. Tichy, Stefan Thonhauser","submitted_at":"2015-02-24T15:44:45Z","abstract_excerpt":"Encouraged by the study of extremal limits for sums of the form $$\\lim_{N\\to\\infty}\\frac{1 }{N}\\sum_{n=1}^N c(x_n,y_n)$$ with uniformly distributed sequences $\\{x_n\\},\\,\\{y_n\\}$ the following extremal problem is of interest $$\\max_{\\gamma}\\int_{[0,1]^2}c(x,y)\\gamma(dx,dy),$$ for probability measures $\\gamma$ on the unit square with uniform marginals, i.e., measures whose distribution function is a copula. The aim of this article is to relate this problem to combinatorial optimization and to the theory of optimal transport. Using different characterizations of maximizing $\\gamma$'s one can give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06839","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"}