{"paper":{"title":"Slow mixing of Glauber Dynamics for the hard-core model on regular bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"David Galvin, Prasad Tetali","submitted_at":"2012-06-14T16:20:38Z","abstract_excerpt":"Let $\\gS=(V,E)$ be a finite, $d$-regular bipartite graph. For any $\\lambda>0$ let $\\pi_\\lambda$ be the probability measure on the independent sets of $\\gS$ in which the set $I$ is chosen with probability proportional to $\\lambda^{|I|}$ ($\\pi_\\lambda$ is the {\\em hard-core measure with activity $\\lambda$ on $\\gS$}). We study the Glauber dynamics, or single-site update Markov chain, whose stationary distribution is $\\pi_\\lambda$. We show that when $\\lambda$ is large enough (as a function of $d$ and the expansion of subsets of single-parity of $V$) then the convergence to stationarity is exponent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3165","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"}