The cutoff phenomenon for Ehrenfest chains

Guan-Yu Chen; Yang Jen Fang; Yuan-Chung Sheu

doi:10.1016/j.spa.2012.05.003

The cutoff phenomenon for Ehrenfest chains

Guan-Yu Chen^*, Yang Jen Fang, Yuan-Chung Sheu

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider families of Ehrenfest chains and provide a simple criterion on the ^Lp-cutoff and the ^Lp-precutoff with specified initial states for 1≤p<∞. For the family with an ^Lp-cutoff, a cutoff time is described and a possible window is given. For the family without an ^Lp-precutoff, the exact order of the ^Lp-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity.

Original language	English
Pages (from-to)	2830-2853
Number of pages	24
Journal	Stochastic Processes and their Applications
Volume	122
Issue number	8
DOIs	https://doi.org/10.1016/j.spa.2012.05.003
State	Published - 1 Aug 2012

Keywords

Cutoff phenomenon
Ehrenfest chains

Access to Document

10.1016/j.spa.2012.05.003

Fingerprint Dive into the research topics of 'The cutoff phenomenon for Ehrenfest chains'. Together they form a unique fingerprint.

Cite this

@article{02c9a3a3404a44cab22383464d863479,

title = "The cutoff phenomenon for Ehrenfest chains",

abstract = "We consider families of Ehrenfest chains and provide a simple criterion on the Lp-cutoff and the Lp-precutoff with specified initial states for 1≤p<∞. For the family with an Lp-cutoff, a cutoff time is described and a possible window is given. For the family without an Lp-precutoff, the exact order of the Lp-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity.",

keywords = "Cutoff phenomenon, Ehrenfest chains",

author = "Guan-Yu Chen and Fang, {Yang Jen} and Yuan-Chung Sheu",

year = "2012",

month = aug,

day = "1",

doi = "10.1016/j.spa.2012.05.003",

language = "English",

volume = "122",

pages = "2830--2853",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "8",

}

TY - JOUR

T1 - The cutoff phenomenon for Ehrenfest chains

AU - Chen, Guan-Yu

AU - Fang, Yang Jen

AU - Sheu, Yuan-Chung

PY - 2012/8/1

Y1 - 2012/8/1

N2 - We consider families of Ehrenfest chains and provide a simple criterion on the Lp-cutoff and the Lp-precutoff with specified initial states for 1≤p<∞. For the family with an Lp-cutoff, a cutoff time is described and a possible window is given. For the family without an Lp-precutoff, the exact order of the Lp-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity.

AB - We consider families of Ehrenfest chains and provide a simple criterion on the Lp-cutoff and the Lp-precutoff with specified initial states for 1≤p<∞. For the family with an Lp-cutoff, a cutoff time is described and a possible window is given. For the family without an Lp-precutoff, the exact order of the Lp-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity.

KW - Cutoff phenomenon

KW - Ehrenfest chains

UR - http://www.scopus.com/inward/record.url?scp=84861695243&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2012.05.003

DO - 10.1016/j.spa.2012.05.003

M3 - Article

AN - SCOPUS:84861695243

VL - 122

SP - 2830

EP - 2853

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 8

ER -