{"paper":{"title":"On the mixing time of simple random walk on the super critical percolation cluster","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Elchanan Mossel, Itai Benjamini","submitted_at":"2000-11-14T21:11:14Z","abstract_excerpt":"We study the robustness under perturbations of mixing times, by studying mixing times of random walks in percolation clusters inside boxes in $\\Z^d$. We show that for $d \\geq 2$ and $p > p_c(\\Z^d)$, the mixing time of simple random walk on the largest cluster inside $\\{-n,...,n\\}^d$ is $\\Theta(n^2)$ - thus the mixing time is robust up to constant factor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011092","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/math/0011092/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"}