{"paper":{"title":"Random subshifts of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Kevin McGoff","submitted_at":"2010-06-07T18:37:11Z","abstract_excerpt":"Let $X$ be an irreducible shift of finite type (SFT) of positive entropy, and let $B_n(X)$ be its set of words of length $n$. Define a random subset $\\omega$ of $B_n(X)$ by independently choosing each word from $B_n(X)$ with some probability $\\alpha$. Let $X_{\\omega}$ be the (random) SFT built from the set $\\omega$. For each $0\\leq \\alpha \\leq1$ and $n$ tending to infinity, we compute the limit of the likelihood that $X_{\\omega}$ is empty, as well as the limiting distribution of entropy for $X_{\\omega}$. For $\\alpha$ near 1 and $n$ tending to infinity, we show that the likelihood that $X_{\\ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1325","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"}