{"paper":{"title":"Convergence of MCMC and Loopy BP in the Tree Uniqueness Region for the Hard-Core Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DM","authors_text":"Charilaos Efthymiou, Daniel Stefankovic, Eric Vigoda, Thomas P. Hayes, Yitong Yin","submitted_at":"2016-04-05T20:57:33Z","abstract_excerpt":"We study the hard-core model defined on independent sets of an input graph where the independent sets are weighted by a parameter $\\lambda>0$. For constant $\\Delta$, previous work of Weitz (2006) established an FPTAS for the partition function for graphs of maximum degree $\\Delta$ when $\\lambda< \\lambda_c(\\Delta)$. The threshold $\\lambda_c(\\Delta)$ is the critical point for the phase transition for uniqueness/non-uniqueness on the infinite $\\Delta$-regular trees. Sly (2010) showed that there is no FPRAS, unless NP=RP, when $\\lambda>\\lambda_c(\\Delta)$. The running time of Weitz's algorithm is e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01422","kind":"arxiv","version":2},"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"}