{"paper":{"title":"Algebraic and arithmetic area for $m$ planar Brownian paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Jean DESBOIS, Stephane Ouvry","submitted_at":"2011-01-21T14:10:02Z","abstract_excerpt":"The leading and next to leading terms of the average arithmetic area $< S(m)>$ enclosed by $m\\to\\infty$ independent closed Brownian planar paths, with a given length $t$ and starting from and ending at the same point, is calculated. The leading term is found to be $< S(m) > \\sim {\\pi t\\over 2}\\ln m$ and the $0$-winding sector arithmetic area inside the $m$ paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4135","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"}