{"paper":{"title":"Random walk on dynamical percolation in Euclidean lattices: separating critical and supercritical regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenlin Gu, Fan Yang, Hao Wu, Jianping Jiang, Yuval Peres, Zhan Shi","submitted_at":"2024-07-21T13:33:53Z","abstract_excerpt":"We study the random walk on dynamical percolation of $\\mathbb{Z}^d$ (resp., the two-dimensional triangular lattice $\\mathcal{T}$), where each edge (resp., each site) can be either open or closed, refreshing its status at rate $\\mu\\in (0,1/e]$. The random walk moves along open edges in $\\mathbb{Z}^d$ (resp., open sites in $\\mathcal{T}$) at rate $1$. For the critical regime $p=p_c$, we prove the following two results: on $\\mathcal{T}$, the mean squared displacement of the random walk from $0$ to $t$ is at most $O(t\\mu^{5/132-\\epsilon})$ for any $\\epsilon>0$; on $\\mathbb{Z}^d$ with $d\\geq 11$, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.15162","kind":"arxiv","version":3},"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/2407.15162/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"}