Electronic Journal of Probability

Cutoff for lamplighter chains on fractals

Amir Dembo, Takashi Kumagai, and Chikara Nakamura

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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

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

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

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Zentralblatt MATH identifier

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

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

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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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