{"paper":{"title":"Stochastic Nash evolution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Dominik Inauen, Govind Menon","submitted_at":"2023-12-11T17:22:12Z","abstract_excerpt":"This paper introduces a probabilistic formulation for the isometric embedding of a Riemannian manifold $(M^n,g)$ into Euclidean space $\\mathbb{R}^q$. Given $\\alpha \\in ]\\tfrac{1}{2},1]$, we show that a $C^{1,\\alpha}$ embedding $u: M \\to \\mathbb{R}^q$ is isometric if and only if the intrinsic and extrinsic constructions of Brownian motion on $u(M)\\subset \\mathbb{R}^q$ yield processes with the same law. The equivalence is first established for smooth embeddings; this is followed by a renormalization procedure for $C^{1,\\alpha}$ embeddings. In particular, we also construct extrinsic Brownian moti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.06541","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.06541/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"}