{"paper":{"title":"Strong spatial mixing in homomorphism spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Raimundo Brice\\~no, Ronnie Pavlov","submitted_at":"2015-10-06T06:58:57Z","abstract_excerpt":"Given a countable graph $\\mathcal{G}$ and a finite graph $\\mathrm{H}$, we consider $\\mathrm{Hom}(\\mathcal{G},\\mathrm{H})$ the set of graph homomorphisms from $\\mathcal{G}$ to $\\mathrm{H}$ and we study Gibbs measures supported on $\\mathrm{Hom}(\\mathcal{G},\\mathrm{H})$ . We develop some sufficient and other necessary conditions on $\\mathrm{Hom}(\\mathcal{G},\\mathrm{H})$ for the existence of Gibbs specifications satisfying strong spatial mixing (with exponential decay rate). We relate this with previous work of Brightwell and Winkler, who showed that a graph $\\mathrm{H}$ has a combinatorial proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01453","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"}