@article{7da61ef7528b44baad289425d52b862a,
title = "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.",
author = "Takeharu Shiraga and Yukiko Yamauchi and Shuji Kijima and Masafumi Yamashita",
note = "Funding Information: ∗Received by the editors August 2, 2016; accepted for publication (in revised form) June 1, 2018; published electronically August 30, 2018. A preliminary version of the results in this paper appeared in Proceedings of the 20th International Computing and Combinatorics Conference, 2014 [44]. http://www.siam.org/journals/sidma/32-3/M108766.html Funding: This work was supported by JSPS KAKENHI Grants 15J03840, 15K15938, 25700002, 15H02666, 17H07116. †Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan (takeharu.shiraga@inf.kyushu-u.ac.jp, yamauchi@inf.kyushu-u.ac.jp, kijima@inf.kyushu-u.ac. jp, mak@inf.kyushu-u.ac.jp). 1See section 3.1, for the detail of the rotor-router model.",
year = "2018",
doi = "10.1137/16M1087667",
language = "English",
volume = "32",
pages = "2180--2193",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}