{"paper":{"title":"Spatial Mixing and Systematic Scan Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cs.DM","authors_text":"Alistair Sinclair, Antonio Blanca, Eric Vigoda, Pietro Caputo","submitted_at":"2016-12-05T22:22:30Z","abstract_excerpt":"We consider spin systems on the integer lattice graph $\\mathbb{Z}^d$ with nearest-neighbor interactions. We develop a combinatorial framework for establishing that exponential decay with distance of spin correlations, specifically the strong spatial mixing condition (SSM), implies rapid mixing of a large class of Markov chains. As a first application of our method we prove that SSM implies $O(\\log n)$ mixing of systematic scan dynamics (under mild conditions) on an $n$-vertex $d$-dimensional cube of the integer lattice graph $\\mathbb{Z}^d$. Systematic scan dynamics are widely employed in pract"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01576","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"}