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arXiv · 1512.00571

Mixing and cut-off in cycle walks

Bob Hough
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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 $A_p \subset \mathbb{Z}/p\mathbb{Z}$.

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Bob Hough. 2015-12-02. Mixing and cut-off in cycle walks. https://doi.org/10.1214/17-ejp108

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