{"paper":{"title":"Uniform measures on braid monoids and dual braid monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.GR","authors_text":"Jean Mairesse, Samy Abbes, S\\'ebastien Gou\\\"ezel, Vincent Jug\\'e","submitted_at":"2016-07-02T21:50:09Z","abstract_excerpt":"We aim at studying the asymptotic properties of typical positive braids, respectively positive dual braids. Denoting by $\\mu_k$ the uniform distribution on positive (dual) braids of length $k$, we prove that the sequence $(\\mu_k)_k$ converges to a unique probability measure $\\mu_{\\infty}$ on infinite positive (dual) braids. The key point is that the limiting measure $\\mu_{\\infty}$ has a Markovian structure which can be described explicitly using the combinatorial properties of braids encapsulated in the M\\\"obius polynomial. As a by-product, we settle a conjecture by Gebhardt and Tawn (J. Algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00565","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":""},"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"}