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} $.
Citation
Robert Hough. "Mixing and cut-off in cycle walks." Electron. J. Probab. 22 1 - 49, 2017. https://doi.org/10.1214/17-EJP108
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