{"paper":{"title":"Mixing time for random walk on supercritical dynamical percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeffrey E. Steif, Perla Sousi, Yuval Peres","submitted_at":"2017-07-24T16:20:14Z","abstract_excerpt":"We consider dynamical percolation on the $d$-dimensional discrete torus of side length $n$, $\\mathbb{Z}_n^d$, where each edge refreshes its status at rate $\\mu=\\mu_n\\le 1/2$ to be open with probability $p$. We study random walk on the torus, where the walker moves at rate $1/(2d)$ along each open edge. In earlier work of two of the authors with A. Stauffer, it was shown that in the subcritical case $p<p_c(\\mathbb{Z}^d)$, the (annealed) mixing time of the walk is $\\Theta(n^2/\\mu)$, and it was conjectured that in the supercritical case $p>p_c(\\mathbb{Z}^d)$, the mixing time is $\\Theta(n^2+1/\\mu)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07632","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"}