{"paper":{"title":"On zeros of Martin-L\\\"of random Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Kelty Allen, Laurent Bienvenu, Theodore Slaman","submitted_at":"2014-05-24T15:24:29Z","abstract_excerpt":"We investigate the sample path properties of Martin-L\\\"of random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-L\\\"of random Brownian path, (2) that the effective dimension of zeroes of a Martin-L\\\"of random Brownian path must be at least 1/2, and conversely that every real with effective dimension greater than 1/2 must be a zero of some Martin-L\\\"of random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6312","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":""},"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"}