{"paper":{"title":"A train track directed random walk on $Out(F_r)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Catherine Pfaff, Ilya Kapovich","submitted_at":"2014-09-29T09:32:46Z","abstract_excerpt":"Several known results, by Rivin, Calegari-Maher and Sisto, show that an element $\\phi_n\\in Out(F_r)$, obtained after $n$ steps of a simple random walk on $Out(F_r)$, is fully irreducible with probability tending to 1 as $n\\to\\infty$. In this paper we construct a natural \"train-track directed\" random walk $\\mathcal W$ on $Out(F_r)$ (where $r\\ge 3$). We show that, for the element $\\phi_n\\in Out(F_r)$, obtained after $n$ steps of this random walk, with asymptotically positive probability the element $\\phi_n$ has the following properties: $\\phi_n$ is an ageometric fully irreducible, which admits a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8044","kind":"arxiv","version":4},"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"}