{"paper":{"title":"On the finite-dimensional marginals of shift-invariant measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"E. Ugalde, J.-M. Gambaudo, J.-R. Chazottes, M. Hochman","submitted_at":"2010-11-10T17:36:08Z","abstract_excerpt":"Let $\\Sigma$ be a finite alphabet, $\\Omega=\\Sigma^{\\mathbb{Z}^{d}}$ equipped with the shift action, and $\\mathcal{I}$ the simplex of shift-invariant measures on $\\Omega$. We study the relation between the restriction $\\mathcal{I}_n$ of $\\mathcal{I}$ to the finite cubes $\\{-n,...,n\\}^d\\subset\\mathbb{Z}^d$, and the polytope of \"locally invariant\" measures $\\mathcal{I}_n^{loc}$. We are especially interested in the geometry of the convex set $\\mathcal{I}_n$ which turns out to be strikingly different when $d=1$ and when $d\\geq 2$. A major role is played by shifts of finite type which are naturally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2442","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"}