{"paper":{"title":"Effective equidistribution of random walks on simple homogeneous spaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.DS","authors_text":"Timoth\\'ee B\\'enard, Weikun He","submitted_at":"2025-11-17T15:47:26Z","abstract_excerpt":"We consider a random walk on a homogeneous space $G/\\Lambda$ where $G$ is a non-compact simple Lie group and $\\Lambda$ is a lattice. The walk is driven by a probability measure $\\mu$ on $G$ whose support generates a Zariski-dense subgroup. We show that the random walk equidistributes towards the Haar measure unless it is trapped in a finite $\\mu$-invariant set. Moreover, under arithmetic assumptions on the pair $(\\Lambda, \\mu)$, we show the convergence occurs at an exponential rate, tempered by the obstructions that the starting point may be high in a cusp or close to a finite orbit.\n  The mai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.13512","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.13512/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"}