{"paper":{"title":"Percolation on the stationary distributions of the voter model with stirring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Valesin, Franco Severo, Jhon Astoquillca, R\\'eka Szab\\'o","submitted_at":"2024-12-12T18:21:33Z","abstract_excerpt":"The voter model with stirring is a variant of the classical voter model on $\\mathbb{Z}^d$ with two possible opinions (0 and 1) that, in addition to copying neighbouring opinions at rate 1, allows voters to interchange their opinions at rate~$\\mathsf{v}$ where~$\\mathsf v \\ge 0$ is the stirring parameter. This model was considered in \\cite{Astoquillca24}, where it was proved that for~$d \\ge 3$ and for any~$\\mathsf{v}$ the set of extremal stationary measures is given by a family~$\\{ \\mu_{\\alpha,\\mathsf{v}}: \\alpha \\in [0,1] \\}$, where~$\\alpha$ is the density of voters with opinion~1. Sampling a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.09532","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.09532/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"}