Deterministic Random Walks for Rapidly Mixing Chains
Abstract
The rotor-router model is a deterministic process analogous to a simple random walk on a graph, and the discrepancy of token configurations between the rotor-router model and its corresponding random walk has been investigated in some contexts. Motivated by general Markov chains beyond simple random walks, this paper investigates a generalized model which imitates a Markov chain (of multiple tokens) possibly containing irrational transition probabilities. We are concerned with the vertexwise discrepancy of the numbers of tokens between the generalized model and its corresponding Markov chain, and present an upper bound of the discrepancy in terms of the mixing time of the Markov chain.
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Information & Authors
Information
Published In
SIAM Journal on Discrete Mathematics
Pages: 2180 - 2193
DOI: 10.1137/16M1087667
ISSN (online): 1095-7146
Copyright
© 2018, Society for Industrial and Applied Mathematics.
History
Submitted: 2 August 2016
Accepted: 1 June 2018
Published online: 30 August 2018
Keywords
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Authors
Funding Information
Japan Society for the Promotion of Science https://doi.org/10.13039/501100001691 : 15J03840, 15K15938, 25700002, 15H02666, 17H07116
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