{"paper":{"title":"Random walks on linear groups satisfying a Schubert condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Weikun He","submitted_at":"2019-05-14T16:15:52Z","abstract_excerpt":"We study random walks on $\\mathrm{GL}_d(\\mathbb{R})$ whose proximal dimension $r$ is larger than $1$ and whose limit set in the Grassmannian $\\mathrm{Gr}_{r,d}(\\mathbb{R})$ is not contained any Schubert variety. These random walks, without being proximal, behave in many ways like proximal ones. Among other results, we establish a H\\\"older-type regularity for the stationary measure on the Grassmannian associated to these random walks. Using this and a generalization of Bourgain's discretized projection theorem, we prove that the proximality assumption in the Bourgain-Furman-Lindenstrauss-Mozes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05695","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":""},"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"}