{"paper":{"title":"Critical probabilities and convergence time of Percolation Probabilistic Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Lorenzo Taggi","submitted_at":"2013-12-25T17:57:51Z","abstract_excerpt":"This paper considers a class of probabilistic cellular automata undergoing a phase transition with an absorbing state. Denoting by ${\\mathcal{U}}(x)$ the neighbourhood of site $x$, the transition probability is $T(\\eta_x = 1 | \\eta_{{\\mathcal{U}}(x)}) = 0$ if $\\eta_{{\\mathcal{U}}(x)}= \\mathbf{0}$ or $p$ otherwise, $\\forall x \\in \\mathbb{Z}$. For any $\\mathcal{U}$ there exists a non-trivial critical probability $p_c({\\mathcal{U}})$ that separates a phase with an absorbing state from a fluctuating phase. This paper studies how the neighbourhood affects the value of $p_c({\\mathcal{U}})$ and provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6990","kind":"arxiv","version":5},"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"}