{"paper":{"title":"Uniform mixing time for Random Walk on Lamplighter Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jason Miller, J\\'ulia Komj\\'athy, Yuval Peres","submitted_at":"2011-09-20T12:31:40Z","abstract_excerpt":"Suppose that $\\CG$ is a finite, connected graph and $X$ is a lazy random walk on $\\CG$. The lamplighter chain $X^\\diamond$ associated with $X$ is the random walk on the wreath product $\\CG^\\diamond = \\Z_2 \\wr \\CG$, the graph whose vertices consist of pairs $(f,x)$ where $f$ is a labeling of the vertices of $\\CG$ by elements of $\\Z_2$ and $x$ is a vertex in $\\CG$. There is an edge between $(f,x)$ and $(g,y)$ in $\\CG^\\diamond$ if and only if $x$ is adjacent to $y$ in $\\CG$ and $f(z) = g(z)$ for all $z \\neq x,y$. In each step, $X^\\diamond$ moves from a configuration $(f,x)$ by updating $x$ to $y$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4281","kind":"arxiv","version":4},"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"}