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    On the Commute Time of Random Walks on Graphs

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    Author
    Northshield, Sam
    Palacios, Jose Luis
    Keyword
    commute time
    cover time
    escape probability
    lollipop graph
    Date Published
    1995
    
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    URI
    http://hdl.handle.net/20.500.12648/1108
    Abstract
    Given a simple random walk on an undirected connected graph, the commute time of the vertices x and y is defined as C(x,y) = ExTy+EyTx. We give a new proof, based on the optional sampling theorem for martingales, of the formula C(x,y) = 1/(Π(y)e(y,x)) in terms of the escape probability e(y,x ) (the probability that once the random walk leaves x, it hits y before it returns to x) and the stationary distribution Π(·). We use this formula for C(x,y) to show that the maximum commute time among all barbell-type graphs in N vertices is attained for the lollipop graph and its value is O[(4N3)/27]
    Citation
    Northshield, S. & Palacios, J.L. (1995). On the Commute Time of Random Walks on Graphs. Brazilian Journal of Probability and Statistics, 9(2).
    Description
    This article has been published in the November 1995 issue of Brazilian Journal of Probability and Statistics.
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