{"paper":{"title":"Langevin deformation for R\\'enyi entropy on Wasserstein space over Riemannian manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rong Lei, Songzi Li, Xiang-Dong Li","submitted_at":"2024-10-27T08:06:57Z","abstract_excerpt":"We introduce the Langevin deformation for the R\\'enyi entropy on the $L^2$-Wasserstein space over $\\mathbb{R}^n$ or a Riemannian manifold, which interpolates between the porous medium equation and the Benamou-Brenier geodesic flow on the $L^2$-Wasserstein space and can be regarded as the compressible Euler equations for isentropic gas with damping. We prove the $W$-entropy-information formulae and the the rigidity theorems for the Langevin deformation for the R\\'enyi entropy on the Wasserstein space over complete Riemannian manifolds with non-negative Ricci curvature or CD$(0, m)$-condition. M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20369","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.20369/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}