Electronic Journal of Probability

Cutoff for lamplighter chains on fractals

Amir Dembo, Takashi Kumagai, and Chikara Nakamura

Full-text: Open access

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).

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 73, 21 pp.

Dates
Received: 8 November 2017
Accepted: 8 July 2018
First available in Project Euclid: 27 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1532678636

Digital Object Identifier
doi:10.1214/18-EJP196

Mathematical Reviews number (MathSciNet)
MR3835479

Zentralblatt MATH identifier
06924685

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 28A80: Fractals [See also 37Fxx] 35K08: Heat kernel

Keywords
Markov chain total variation mixing time cutoff phenomenon lamplighter group heat kernel fractal graphs late points

Rights
Creative Commons Attribution 4.0 International License.

Citation

Dembo, Amir; Kumagai, Takashi; Nakamura, Chikara. Cutoff for lamplighter chains on fractals. Electron. J. Probab. 23 (2018), paper no. 73, 21 pp. doi:10.1214/18-EJP196. https://projecteuclid.org/euclid.ejp/1532678636


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