{"paper":{"title":"Improved Mixing Condition on the Grid for Counting and Sampling Independent Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.PR","authors_text":"Eric Vigoda, Jinwoo Shin, Linji Yang, Prasad Tetali, Ricardo Restrepo","submitted_at":"2011-05-04T19:52:13Z","abstract_excerpt":"We study the hard-core model defined on independent sets, where each independent set I in a graph G is weighted proportionally to $\\lambda^{|I|}$, for a positive real parameter $\\lambda$. For large $\\lambda$, computing the partition function (namely, the normalizing constant which makes the weighting a probability distribution on a finite graph) on graphs of maximum degree $D\\ge 3$, is a well known computationally challenging problem. More concretely, let $\\lambda_c(T_D)$ denote the critical value for the so-called uniqueness threshold of the hard-core model on the infinite D-regular tree; rec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0914","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"}