Electronic Journal of Probability

Mixing and cut-off in cycle walks

Robert Hough

Abstract

Given a sequence $(\mathfrak{X} _i, \mathscr{K} _i)_{i=1}^\infty$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and the cut-off phenomenon in the total variation metric in the case of random walk on the groups $\mathbb{Z} /p\mathbb{Z}$, $p$ prime, with driving measure uniform on a symmetric generating set $A \subset \mathbb{Z} /p\mathbb{Z}$.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 90, 49 pp.

Dates
Accepted: 15 September 2017
First available in Project Euclid: 18 October 2017

https://projecteuclid.org/euclid.ejp/1508292261

Digital Object Identifier
doi:10.1214/17-EJP108

Mathematical Reviews number (MathSciNet)
MR3718718

Zentralblatt MATH identifier
1378.60073

Citation

Hough, Robert. Mixing and cut-off in cycle walks. Electron. J. Probab. 22 (2017), paper no. 90, 49 pp. doi:10.1214/17-EJP108. https://projecteuclid.org/euclid.ejp/1508292261

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