Cover times, blanket times, and majorizing measures
نویسندگان
چکیده
منابع مشابه
Blanket times and the Gaussian Free Field
The blanket time of a random walk on a graph G is the expected time until the proportion of time spent at each vertex approximates the stationary distribution. In 1996, Winkler and Zuckerman conjectured that the blanket time is of the same order as the cover time. Ding, Lee and Peres proved this conjecture in 2010 by relating both terms to the maximum of the Gaussian free field on G. We outline...
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The maximal mean hitting time max i;j E i T j arises in many contexts. In Chapter 5 we saw how to compute this in various simple examples, and the discussion of in Chapter 4 indicated general methods (in particular, the electrical resistance story) for upper bounding this quantity. But what we've done so far doesn't answer questions like \how large can be, for random walk on a n-vertex graph". ...
متن کاملExponential concentration of cover times
We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding, Lee, and Peres [8] and Ding [7]. The estimate is asymptotically sharp as the ratio of hitting time to cover time goes to zero. The bounds are obtained by showing a stochastic domination in the generalized second Ray-Knight theorem, which was shown to imp...
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Under a natural hypothesis, the cover time for a finite Markov chain can be approximated by its expectation, as the size of state space tends to infinity. This result is deduced from an abstract result concerning covering an unstructured set by i.i.d. arbitrarily-distributed random subsets. running head: Threshold limits for cover times. key words. cover time, Markov chain, random walk on graph...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.175.3.8