{"paper":{"title":"Randomized Computation of Continuous Data: Is Brownian Motion Computable?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","cs.NA"],"primary_cat":"math.NA","authors_text":"Donghyun Lim, Hyunwoo Lee, Martin Ziegler, Matthias Schr\\\"oder, Sewon Park, Willem Fouch\\'e","submitted_at":"2019-06-16T13:32:14Z","abstract_excerpt":"We consider randomized computation of continuous data in the sense of Computable Analysis. Our first contribution formally confirms that it is no loss of generality to take as sample space the Cantor space of infinite FAIR coin flips. This extends [Schr\\\"oder&Simpson'05] and [Hoyrup&Rojas'09] considering sequences of suitably and adaptively BIASED coins.\n  Our second contribution is concerned with 1D Brownian Motion (aka Wiener Process), a probability distribution on the space of continuous functions f:[0,1]->R with f(0)=0 whose computability has been conjectured [Davie&Fouch\\'e'13; arXiv:1409"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06684","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"}