{"paper":{"title":"Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexandre Stauffer, Jeffrey E. Steif, Yuval Peres","submitted_at":"2013-08-28T16:03:50Z","abstract_excerpt":"We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate \\mu\\ while at the same time a random walker moves on G at rate 1 but only along edges which are open. On the d-dimensional torus with side length n, we prove that in the subcritical regime, the mixing times for both the full system and the random walker are n^2/\\mu\\ up to constants. We also obtain results concerning mean squared displacement and hitting times. Finally, we show that the usual recurrence transience dichotomy for the latti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6193","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"}