{"paper":{"title":"Rigidity and equidistribution of random walks by diffeomorphisms near the conservative regime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Timoth\\'ee B\\'enard, Zhiyuan Zhang","submitted_at":"2026-05-26T13:28:15Z","abstract_excerpt":"We consider a random walk on a closed manifold $M$ driven by a probability measure $\\mu$ on the space of $C^2$ diffeomorphisms. Provided $\\mu$ has compact support, satisfies certain gap and pinching conditions, and is weak-$*$ close to a volume-preserving measure, we prove that $M$ carries a unique atom-free stationary probability measure $\\Upsilon_{\\mu}$. This measure has full Frostman dimension and coincides with volume in the volume-preserving setting. Moreover, for every $x\\in M$, the $n$-step distribution $\\mu^{*n} * \\delta_x$ converges to $\\Upsilon_{\\mu}$ unless $x$ is contained in a fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27008","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/2605.27008/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"}