{"paper":{"title":"A Concrete Estimate For The Weak Poincare Inequality On Loop Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Bo Wu, Xin Chen, Xue-Mei Li","submitted_at":"2009-10-26T12:26:57Z","abstract_excerpt":"The aim of the paper is to study the pinned Wiener measure on the loop space over a simply connected compact Riemannian manifold together with the Hilbert space structure induced by Mallianvin calculus and the induced Ornstein- Uhlenbeck operator. We give a concrete estimate for the weak Poincare inequality for the O-U Dirichlet form on loop space over simply connected compact Riemannian manifold with strict positive Ricci curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4846","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"}