Uniformity of the uncovered set of random walk and cutoff for lamplighter chains
نویسندگان
چکیده
منابع مشابه
Uniformity of the Uncovered Set of Random Walk and Cutoff for Lamplighter Chains
We show that the measure on markings of Zn, d ≥ 3, with elements of {0,1} given by i.i.d. fair coin flips on the range R of a random walk X run until time T and 0 otherwise becomes indistinguishable from the uniform measure on such markings at the threshold T = 1 2 Tcov(Z d n). As a consequence of our methods, we show that the total variation mixing time of the random walk on the lamplighter gr...
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Uniform Mixing Time for Random Walk on Lamplighter Graphs
Suppose that G is a finite, connected graph and X is a lazy random walk on G. The lamplighter chain X associated with X is the random walk on the wreath product G = Z2 oG, the graph whose vertices consist of pairs (f, x) where f is a labeling of the vertices of G by elements of Z2 and x is a vertex in G. There is an edge between (f, x) and (g, y) in G if and only if x is adjacent to y in G and ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2012
ISSN: 0091-1798
DOI: 10.1214/10-aop624