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Deterministic Random Walks for Rapidly Mixing Chains
The rotor-router model is a deterministic process analogous to a simple
random walk on a graph. This paper is concerned with a generalized model,
functional-router model, which imitates a Markov chain possibly containing
irrational transition probabilities. We investigate the discrepancy of the
number of tokens at a single vertex between the functional-router model and its
corresponding Markov chain, and give an upper bound in terms of the mixing time
of the Markov chain