Deterministic random walks for rapidly mixing chains

Takeharu Shiraga, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita

Research output: Contribution to journalArticle

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 - Jan 1 2018

Fingerprint

Random walk
Markov chain
Discrepancy
Simple Random Walk
Router
Rotor
Mixing Time
Transition Probability
Model
Upper bound
Configuration
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Deterministic random walks for rapidly mixing chains. / Shiraga, Takeharu; Yamauchi, Yukiko; Kijima, Shuji; Yamashita, Masafumi.

In: SIAM Journal on Discrete Mathematics, Vol. 32, No. 3, 01.01.2018, p. 2180-2193.

Research output: Contribution to journalArticle

Shiraga, Takeharu ; Yamauchi, Yukiko ; Kijima, Shuji ; Yamashita, Masafumi. / Deterministic random walks for rapidly mixing chains. In: SIAM Journal on Discrete Mathematics. 2018 ; Vol. 32, No. 3. pp. 2180-2193.
@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",
year = "2018",
month = "1",
day = "1",
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",

}

TY - JOUR

T1 - Deterministic random walks for rapidly mixing chains

AU - Shiraga, Takeharu

AU - Yamauchi, Yukiko

AU - Kijima, Shuji

AU - Yamashita, Masafumi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85053896504&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053896504&partnerID=8YFLogxK

U2 - 10.1137/16M1087667

DO - 10.1137/16M1087667

M3 - Article

AN - SCOPUS:85053896504

VL - 32

SP - 2180

EP - 2193

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 3

ER -