A Chernoff Bound for Random Walks on Expander Graphs

@article{Gillman1998ACB,
  title={A Chernoff Bound for Random Walks on Expander Graphs},
  author={David Gillman},
  journal={SIAM J. Comput.},
  year={1998},
  volume={27},
  pages={1203-1220}
}
We consider a finite random walk on a weighted graph G; we show that the sample average of visits to a set of vertices A converges to the stationary probability n(A) with error probability exponentially small in the length of the random walk and the square of the size of the deviation from a(A) . The exponential bound is in terms of the expansion of G and improves previous results of [Ald87, LS, AKS]. We show that the method of taking the sample average from one trajectory is a more eficient… CONTINUE READING
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