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 eficientâ€¦Â CONTINUE READING