{"paper":{"title":"Poincar\\'e inequality for Markov random fields via disagreement percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"F. Redig, F. V\\\"ollering, J.-R. Chazottes","submitted_at":"2010-12-11T21:29:52Z","abstract_excerpt":"We consider Markov random fields of discrete spins on the lattice $\\Zd$. We use a technique of coupling of conditional distributions. If under the coupling the disagreement cluster is \"sufficiently\" subcritical, then we prove the Poincar\\'e inequality. In the whole subcritical regime, we have a weak Poincar\\'e inequality and corresponding polynomial upper bound for the relaxation of the associated Glauber dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2489","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":""},"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"}