{"paper":{"title":"The exclusion process mixes (almost) faster than independent particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathan Hermon, Richard Pymar","submitted_at":"2018-08-31T17:20:34Z","abstract_excerpt":"Oliveira conjectured that the order of the mixing time of the exclusion process with $k$-particles on an arbitrary $n$-vertex graph is at most that of the mixing-time of $k$ independent particles. We verify this up to a constant factor for $d$-regular graphs when each edge rings at rate $1/d$ in various cases: (1) when $d = \\Omega( \\log_{n/k} n)$, (2) when $\\mathrm{gap}:=$ the spectral-gap of a single walk is $ O ( 1/\\log^4 n) $ and $k \\ge n^{\\Omega(1)}$, (3) when $k \\asymp n^{a}$ for some constant $0<a<1$. In these cases our analysis yields a probabilistic proof of a weaker version of Aldous'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10846","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.10846/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}