{"paper":{"title":"Zero-temperature Glauber dynamics on the 3-regular tree and the median process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arnab Sen, Michael Damron","submitted_at":"2019-04-25T23:30:37Z","abstract_excerpt":"In zero-temperature Glauber dynamics, vertices of a graph are given i.i.d.~initial spins $\\sigma_x(0)$ from $\\{-1,+1\\}$ with $\\mathbb{P}_p(\\sigma_x(0) = +1)=p$, and they update their spins at the arrival times of i.i.d. Poisson processes to agree with a majority of their neighbors. We study this process on the 3-regular tree $\\mathbb{T}_3$, where it is known that the critical threshold $p_c$, below which $\\mathbb{P}_p$-a.s. all spins fixate to $-1$, is strictly less than $1/2$. Defining $\\theta(p)$ to be the $\\mathbb{P}_p$-probability that a vertex fixates to $+1$, we show that $\\theta$ is a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11625","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":""},"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"}