Random Walks on Highly Symmetric Graphs

  title={Random Walks on Highly Symmetric Graphs},
  author={Luc Devroye and Amine Sbihi},
We consider uniform random walks on finite graphs with n nodes. When the hitting times are symmetric, the expected covering time is at least 89 log n O(n log log n) uniformly over all such graphs. We also obtain bounds for the covering times in terms of the eigenvalues of the transition matrix of the Markov chain. For distance-regular graphs, a general lower bound of ( n 1 ) l o g n is obtained. For hypercubes and binomial coefficient graphs, the limit law of the covering time is obtained as… CONTINUE READING