Open Access
2018 Cutoff for lamplighter chains on fractals
Amir Dembo, Takashi Kumagai, Chikara Nakamura
Electron. J. Probab. 23: 1-21 (2018). DOI: 10.1214/18-EJP196


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).


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Amir Dembo. Takashi Kumagai. Chikara Nakamura. "Cutoff for lamplighter chains on fractals." Electron. J. Probab. 23 1 - 21, 2018.


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

zbMATH: 06924685
MathSciNet: MR3835479
Digital Object Identifier: 10.1214/18-EJP196

Primary: 60J10
Secondary: 28A80 , 35K08

Keywords: Cutoff phenomenon , fractal graphs , heat kernel , lamplighter group , late points , Markov chain , mixing time , Total variation

Vol.23 • 2018
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