{"paper":{"title":"Antithetic variates in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Joan-Andreu L\\'azaro-Cam\\'i, Sebastian del Ba\\~no Rollin","submitted_at":"2009-02-24T18:26:17Z","abstract_excerpt":"We introduce the concept of multidimensional antithetic as the absolute minimum of the covariance defined on the orthogonal group by $A\\mapsto Cov(f(\\xi),f(A\\xi))$ where $\\xi$ is a standard $N$-dimensional normal random variable and $f:\\mathbb{R}^{N}\\to\\mathbb{R}$ is an almost everywhere differentiable function. The antithetic matrix is designed to optimise the calculation of $E[f(\\xi)]$ in a Monte Carlo simulation. We present an iterative annealing algorithm that dynamically incorporates the estimation of the antithetic matrix within the Monte Carlo calculation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4211","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0902.4211/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}