Mixing and cut-off in cycle walks

Abstract

Given a sequence $({\mathfrak{X}}_i,{\mathcal{K}}_i{)}_{i=1}^{\infty }$ 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 $A_p\subset \mathbb{Z}/p\mathbb{Z}$.

Published version, updated acknowledgement of financial support

References in corpus (1)

• Separation cut-offs for birth and death chains

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