{"paper":{"title":"Self-repelling diffusions on a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Carl-Erik Gauthier, Michel Bena\\\"im","submitted_at":"2015-05-21T10:04:47Z","abstract_excerpt":"Let M be a compact connected oriented Riemannian manifold. The purpose of this paper is to investigate the long time behavior of a degenerate stochastic differential equation on the state space $M\\times \\mathbb{R}^{n}$; which is obtained via a natural change of variable from a self-repelling diffusion taking the form $$dX_{t}= \\sigma dB_{t}(X_t) -\\int_{0}^{t}\\nabla V_{X_s}(X_{t})dsdt,\\qquad X_{0}=x$$ where $\\{B_t\\}$ is a Brownian vector field on $M$, $\\sigma >0$ and $V_x(y) = V(x,y)$ is a diagonal Mercer kernel.\n  We prove that the induced semi-group enjoys the strong Feller property and has a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05664","kind":"arxiv","version":3},"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"}