Electronic Journal of Probability

Mixing and cut-off in cycle walks

Robert Hough

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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

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

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

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Zentralblatt MATH identifier

Primary: 60B10: Convergence of probability measures
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60G50: Sums of independent random variables; random walks 60J60: Diffusion processes [See also 58J65] 11H06: Lattices and convex bodies [See also 11P21, 52C05, 52C07] 11A63: Radix representation; digital problems {For metric results, see 11K16}

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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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