## Electronic Journal of Probability

### 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).

#### Article information

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

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

https://projecteuclid.org/euclid.ejp/1532678636

Digital Object Identifier
doi:10.1214/18-EJP196

Mathematical Reviews number (MathSciNet)
MR3835479

Zentralblatt MATH identifier
06924685

#### 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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