Deterministic random walks for rapidly mixing chains

Takeharu Shiraga, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)2180-2193
Number of pages14
JournalSIAM Journal on Discrete Mathematics
Volume32
Issue number3
DOIs
Publication statusPublished - 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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