{"paper":{"title":"Cutoff for congestion dynamics and related generalized exclusion processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.PR","authors_text":"Ryokichi Tanaka","submitted_at":"2025-02-09T23:30:22Z","abstract_excerpt":"We consider congestion dynamics with $n$ players and $Q$ resources under the constraint that the number of each resource is $\\kappa$ and that $n<\\kappa Q$ in the regime that $n$ and $\\kappa$ diverge but $Q$ is fixed with $n=\\lfloor{\\rho \\kappa Q\\rfloor}$ for a fixed constant $\\rho \\in (0, 1/2]$. We show that the Glauber dynamics and its unlabeled version exhibit cutoff at time $(1/2)n \\log n$ and $(1/2)(1-\\rho)n\\log n$ in total variation respectively. The unlabeled version is a special case of natural Markov chains for sampling from log M-concave distributions. We also show that a family of Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06071","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06071/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"}