{"paper":{"title":"Factor maps and embeddings for random $\\mathbb{Z}^d$ shifts of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kevin McGoff, Ronnie Pavlov","submitted_at":"2017-04-28T19:12:15Z","abstract_excerpt":"For any $d \\geq 1$, random $\\mathbb{Z}^d$ shifts of finite type (SFTs) were defined in previous work of the authors. For a parameter $\\alpha \\in [0,1]$, an alphabet $\\mathcal{A}$, and a scale $n \\in \\mathbb{N}$, one obtains a distribution of random $\\mathbb{Z}^d$ SFTs by randomly and independently forbidding each pattern of shape $\\{1,\\dots,n\\}^d$ with probability $1-\\alpha$ from the full shift on $\\mathcal{A}$. We prove two main results concerning random $\\mathbb{Z}^d$ SFTs. First, we establish sufficient conditions on $\\alpha$, $\\mathcal{A}$, and a $\\mathbb{Z}^d$ subshift $Y$ so that a rando"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00042","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"}