{"paper":{"title":"Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC","math.PR"],"primary_cat":"math.DG","authors_text":"Luca Rizzi, Robert Neel, Ugo Boscain","submitted_at":"2015-03-02T21:00:13Z","abstract_excerpt":"On a sub-Riemannian manifold we define two type of Laplacians. The \\emph{macroscopic Laplacian} $\\Delta_\\omega$, as the divergence of the horizontal gradient, once a volume $\\omega$ is fixed, and the \\emph{microscopic Laplacian}, as the operator associated with a sequence of geodesic random walks. We consider a general class of random walks, where \\emph{all} sub-Riemannian geodesics are taken in account. This operator depends only on the choice of a complement $\\mathbf{c}$ to the sub-Riemannian distribution, and is denoted $L^c$.\n  We address the problem of equivalence of the two operators. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00725","kind":"arxiv","version":4},"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"}