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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.4405","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-22T04:20:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0e3c898a38595a967e361b58a8abe0c08da4caf3d9d173d5755d8f8d149c7b42","abstract_canon_sha256":"c56c40c6d1607c1d5ed6a0fb247ed04205b58d3290055de37499d00ea1633c02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:40.712443Z","signature_b64":"umV77E3bBl9QpsiQmtOzOQlYdTrQShixndio/c0FIfsI5FeoNPWrkUTybXFl6luwZYycCTJP+JGkf/eyZuGOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c060195c8942386f46b13978905be114d0037b887a527c0d172493d55ff1251f","last_reissued_at":"2026-05-18T01:33:40.711964Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:40.711964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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