Summary
Consider a random walk on a finite group G. Suppose that the time taken for the transition probabilities to approach the uniform distribution is small compared with #G. Then the time taken for the random walk to visit every state is approximately R#G·log(#G), where R is the mean number of returns to the initial state in the short term.
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Research supported by National Science Foundation grant MCS 80-02698
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Aldous, D.J. On the time taken by random walks on finite groups to visit every state. Z. Wahrscheinlichkeitstheorie verw Gebiete 62, 361–374 (1983). https://doi.org/10.1007/BF00535260
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DOI: https://doi.org/10.1007/BF00535260