Cutoff for lamplighter chains on fractals

Amir Dembo; Takashi Kumagai; Chikara Nakamura

doi:10.1214/18-EJP196

Cutoff for lamplighter chains on fractals

Amir Dembo, Takashi Kumagai, Chikara Nakamura

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

1 Citation (Scopus)

Abstract

We show that the total-variation mixing time of the lamplighter random walk on fractal graphs exhibit sharp cutoff when the underlying graph is transient (namely of spectral dimension greater than two). In contrast, we show that such cutoff can not occur for strongly recurrent underlying graphs (i.e. of spectral dimension less than two).

Original language	English
Article number	73
Journal	Electronic Journal of Probability
Volume	23
DOIs	https://doi.org/10.1214/18-EJP196
Publication status	Published - 2018
Externally published	Yes

Keywords

Cutoff phenomenon
Fractal graphs
Heat kernel
Lamplighter group
Late points
Markov chain
Mixing time
Total variation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/18-EJP196

Cite this

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title = "Cutoff for lamplighter chains on fractals",

abstract = "We show that the total-variation mixing time of the lamplighter random walk on fractal graphs exhibit sharp cutoff when the underlying graph is transient (namely of spectral dimension greater than two). In contrast, we show that such cutoff can not occur for strongly recurrent underlying graphs (i.e. of spectral dimension less than two).",

keywords = "Cutoff phenomenon, Fractal graphs, Heat kernel, Lamplighter group, Late points, Markov chain, Mixing time, Total variation",

author = "Amir Dembo and Takashi Kumagai and Chikara Nakamura",

note = "Funding Information: This project was supported by the Kyoto University Top Global University (KTGU) Project. The research of Amir Dembo was partially supported by NSF Grant Number DMS-1613091. Takashi Kumagai was partially supported by JSPS KAKENHI (A) 25247007 and 17H01093. Chikara Nakamura was partially supported by JSPS KAKENHI Grant Number 15J02838. Publisher Copyright: {\textcopyright} 2018, University of Washington. All rights reserved.",

year = "2018",

doi = "10.1214/18-EJP196",

language = "English",

volume = "23",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

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T1 - Cutoff for lamplighter chains on fractals

AU - Dembo, Amir

AU - Kumagai, Takashi

AU - Nakamura, Chikara

N1 - Funding Information: This project was supported by the Kyoto University Top Global University (KTGU) Project. The research of Amir Dembo was partially supported by NSF Grant Number DMS-1613091. Takashi Kumagai was partially supported by JSPS KAKENHI (A) 25247007 and 17H01093. Chikara Nakamura was partially supported by JSPS KAKENHI Grant Number 15J02838. Publisher Copyright: © 2018, University of Washington. All rights reserved.

PY - 2018

Y1 - 2018

N2 - We show that the total-variation mixing time of the lamplighter random walk on fractal graphs exhibit sharp cutoff when the underlying graph is transient (namely of spectral dimension greater than two). In contrast, we show that such cutoff can not occur for strongly recurrent underlying graphs (i.e. of spectral dimension less than two).

AB - We show that the total-variation mixing time of the lamplighter random walk on fractal graphs exhibit sharp cutoff when the underlying graph is transient (namely of spectral dimension greater than two). In contrast, we show that such cutoff can not occur for strongly recurrent underlying graphs (i.e. of spectral dimension less than two).

KW - Cutoff phenomenon

KW - Fractal graphs

KW - Heat kernel

KW - Lamplighter group

KW - Late points

KW - Markov chain

KW - Mixing time

KW - Total variation

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VL - 23

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 73

ER -

Cutoff for lamplighter chains on fractals

Abstract

Keywords

ASJC Scopus subject areas

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