Open Access
2017 Mixing and cut-off in cycle walks
Robert Hough
Electron. J. Probab. 22: 1-49 (2017). DOI: 10.1214/17-EJP108


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} $.


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Robert Hough. "Mixing and cut-off in cycle walks." Electron. J. Probab. 22 1 - 49, 2017.


Received: 20 June 2016; Accepted: 15 September 2017; Published: 2017
First available in Project Euclid: 18 October 2017

zbMATH: 1378.60073
MathSciNet: MR3718718
Digital Object Identifier: 10.1214/17-EJP108

Primary: 60B10
Secondary: 11A63 , 11H06 , 60B15 , 60G50 , 60J60

Keywords: cut-off phenomenon , embedded hypercube , random lattice , Random walk on a group

Vol.22 • 2017
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