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Lower bounds for covering times for reversible Markov chains and random walks on graphs

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Abstract

For simple random walk on aN-vertex graph, the mean time to cover all vertices is at leastcN log(N), wherec>0 is an absolute constant. This is deduced from a more general result about stationary finite-state reversible Markov chains. Under weak conditions, the covering time for such processes is at leastc times the covering time for the corresponding i.i.d. process.

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References

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Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, California

    David J. Aldous

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  1. David J. Aldous
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Aldous, D.J. Lower bounds for covering times for reversible Markov chains and random walks on graphs. J Theor Probab 2, 91–100 (1989). https://doi.org/10.1007/BF01048272

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  • DOI: https://doi.org/10.1007/BF01048272

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