{"paper":{"title":"Wiener Process with Reflection in Non-Smooth Narrow Tubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Konstantinos Spiliopoulos","submitted_at":"2010-04-18T01:46:23Z","abstract_excerpt":"Wiener process with instantaneous reflection in narrow tubes of width {\\epsilon}<<1 around axis x  is considered in this paper. The tube is assumed to be (asymptotically) non-smooth in the following sense. Let $V^{\\epsilon}(x)$ be the volume of the cross-section of the tube. We assume that $V^{\\epsilon}(x)/{\\epsilon}$ converges in an appropriate sense to a non-smooth function as {\\epsilon}->0. This limiting function can be composed by smooth functions, step functions and also the Dirac delta distribution. Under this assumption we prove that the x-component of the Wiener process converges weakl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2991","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"}