{"paper":{"title":"Fixation for Two-Dimensional $\\mathcal U$-ISING and $\\mathcal U$-VOTER Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Daniel Blanquicett","submitted_at":"2020-03-05T03:56:04Z","abstract_excerpt":"Given a finite family $\\mathcal U$ of finite subsets of $\\mathbb Z^d\\setminus \\{0\\}$, the $\\mathcal U$-$voter\\ dynamics$ in the space of configurations $\\{+,-\\}^{\\mathbb Z^d}$ is defined as follows: every $v\\in\\mathbb Z^d$ has an independent exponential random clock, and when the clock at $v$ rings, the vertex $v$ chooses $X\\in\\mathcal U$ uniformly at random. If the set $v+X$ is entirely in state $+$ (resp. $-$), then the state of $v$ updates to $+$ (resp. $-$), otherwise nothing happens. The $critical\\ probability$ $p_c^{\\text{vot}}(\\mathbb Z^d,\\mathcal U)$ for this model is the infimum over "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.02420","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.02420/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}