{"paper":{"title":"Dispersion and limit theorems for random walks associated with hypergeometric functions of type BC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","math.RT"],"primary_cat":"math.CA","authors_text":"Michael Voit","submitted_at":"2015-06-16T11:25:53Z","abstract_excerpt":"The spherical functions of the noncompact Grassmann manifolds $G_{p,q}(\\mathbb F)=G/K$ over the (skew-)fields $\\mathbb F=\\mathbb R, \\mathbb C, \\mathbb H$ with rank $q\\ge1$ and dimension parameter $p>q$ can be described as Heckman-Opdam hypergeometric functions of type BC, where the double coset space $G//K$ is identified with the Weyl chamber $ C_q^B\\subset \\mathbb R^q$ of type B. The corresponding product formulas and Harish-Chandra integral representations were recently written down by M. R\\\"osler and the author in an explicit way such that both formulas can be extended analytically to all r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04925","kind":"arxiv","version":2},"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"}