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    On the Commute Time of Random Walks on Graphs

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    Date
    1995
    Author
    Northshield, Sam
    Palacios, Jose Luis
    Publisher
    Brazilian Journal of Probability and Statistics
    Metadata
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    Subject
    commute time
    cover time
    escape probability
    lollipop graph
    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]
    Description
    This article has been published in the November 1995 issue of Brazilian Journal of Probability and Statistics.
    URI
    http://hdl.handle.net/1951/69946
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    • Mathematics Faculty Work [20]

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