{"paper":{"title":"Mixing Times of Self-Organizing Lists and Biased Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Amanda Pascoe Streib, Dana Randall, Prateek Bhakta, Sarah Miracle","submitted_at":"2012-04-15T06:21:46Z","abstract_excerpt":"Sampling permutations from S_n is a fundamental problem from probability theory. The nearest neighbor transposition chain \\cal{M}}_{nn} is known to converge in time \\Theta(n^3 \\log n) in the uniform case and time \\Theta(n^2) in the constant bias case, in which we put adjacent elements in order with probability p \\neq 1/2 and out of order with probability 1-p. Here we consider the variable bias case where we put adjacent elements x<y in order with probability p{x,y} and out of order with probability 1-p_{x,y}. The problem of bounding the mixing rate of M_{nn} was posed by Fill and was motivated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3239","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":""},"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"}