{"paper":{"title":"Mixing of the exclusion process with small bias","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David A. Levin, Yuval Peres","submitted_at":"2016-08-11T23:05:04Z","abstract_excerpt":"We analyze the mixing behavior of the biased exclusion process on a path of length $n$ as the bias $\\beta_n$ tends to $0$ as $n \\to \\infty$. We show that the sequence of chains has a pre-cutoff, and interpolates between the unbiased exclusion and the process with constant bias. As the bias increases, the mixing time undergoes two phase transitions: one when $\\beta_n$ is of order $1/n$, and the other when $\\beta_n$ is order $\\log n/n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03633","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"}