{"paper":{"title":"A simple proof of rapid mixing on random regular graphs beyond uniqueness","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.PR","authors_text":"Andreas G\\\"obel, Leon Schiller, Marcus Michelen, Marcus Pappik, Matthew Jenssen, Will Perkins","submitted_at":"2026-06-25T20:48:28Z","abstract_excerpt":"A recent breakthrough of Chen, Chen, Chen, Yin, and Zhang shows rapid mixing for Glauber dynamics for the hard-core model on random regular graphs beyond the tree uniqueness threshold. Their approach builds upon the literature of various local-to-global techniques and applies to a more general setting of discrete distributions supported on downward-closed set families. We give a short and self-contained proof via a Bochner--Bakry--\\'{E}mery approach and directly show a Poincar\\'e inequality by expanding the Dirichlet form in terms of the $L^2$-norm of the generator applied to a test function a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27545","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/2606.27545/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"}