{"paper":{"title":"Random Subwords and Billiard Walks in Affine Weyl Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Colin Defant, Elchanan Mossel, Pakawut Jiradilok","submitted_at":"2025-01-19T16:11:18Z","abstract_excerpt":"Let $W$ be an irreducible affine Weyl group, and let $\\mathsf{b}$ be a finite word over the alphabet of simple reflections of $W$. Fix a probability $p\\in(0,1)$. For each integer $K\\geq 0$, let $\\mathsf{sub}_p(\\mathsf{b}^K)$ be the random subword of $\\mathsf{b}^K$ obtained by deleting each letter independently with probability $1-p$. Let $v_p(\\mathsf{b}^K)$ be the element of $W$ represented by $\\mathsf{sub}_p(\\mathsf{b}^K)$. One can view $v_p(\\mathsf{b}^K)$ geometrically as a random alcove; in many cases, this alcove can be seen as the location after a certain amount of time of a random billia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11095","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/2501.11095/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"}