{"paper":{"title":"Sharp phase transition in the random stirring model on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alan Hammond","submitted_at":"2012-02-07T00:30:28Z","abstract_excerpt":"We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists d_0 such that, for any d \\geq d_0, the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree d almost surely contains an infinite cycle consists of a semi-infinite interval. The critical point at the left-hand end of this interval is at least 1/d + 1/(2d^2) and at most 1/d + 2/(d^2).\n  This version is a major revision, with a much shorter proof. Principal among the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1322","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"}