{"paper":{"title":"The shape of a random affine Weyl group element and random core partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Thomas Lam","submitted_at":"2011-02-22T04:20:28Z","abstract_excerpt":"Let $W$ be a finite Weyl group and ${\\hat{W}}$ be the corresponding affine Weyl group. We show that a large element in ${\\hat{W}}$, randomly generated by (reduced) multiplication by simple generators, almost surely has one of $|W|$-specific shapes. Equivalently, a reduced random walk in the regions of the affine Coxeter arrangement asymptotically approaches one of $|W|$-many directions. The coordinates of this direction, together with the probabilities of each direction can be calculated via a Markov chain on $W$. Our results, applied to type $\\tilde{A}_{n-1}$, show that a large random $n$-cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4405","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":""},"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"}