{"paper":{"title":"Application of an averaging principle on foliated diffusions: topology of the leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paulo R. Ruffino","submitted_at":"2014-08-06T00:55:19Z","abstract_excerpt":"We consider an $\\epsilon K$ transversal perturbing vector field in a foliated Brownian motion defined in a foliated tubular neighbourhood of an embedded compact submanifold in $\\R^3$. We study the effective behaviour of the system under this $\\epsilon$ perturbation. If the perturbing vector field $K$ is proportional to the Gaussian curvature at the corresponding leaf, we have that the transversal component, after rescaling the time by $t/\\epsilon$, approaches a linear increasing behaviour proportional to the Euler characteristic of $M$, as $\\epsilon$ goes to zero. An estimate of the rate of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1154","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"}