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Stationary distribution and cover time of random walks on random digraphs

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posted on 10.11.2011, 00:00 by Colin Cooper, Alan FriezeAlan Frieze

We study properties of a simple random walk on the random digraph Dn,p when np = d log n , d>1.

We prove that whp the value πv of the stationary distribution at vertex v is asymptotic to deg(v)/m where deg(v) is the in-degree of v and m=n(n−1)p is the expected number of edges of Dn,p. If d=d(n)→∞ with n, the stationary distribution is asymptotically uniform whp.

Using this result we prove that, for d>1, whp the cover time of Dn,p is asymptotic to d log(d/(d − 1))n log n . If d=d(n)→∞ with n , then the cover time is asymptotic to n log n

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Publisher Statement

This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.jctb.2011.11.001

Date

10/11/2011

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