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arXiv · 1407.3580

Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod $n$

Michael E. Bate·Stephen B. Connor
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Abstract

We analyse a random walk on the ring of integers mod $n$, which at each time point can make an additive `step' or a multiplicative `jump'. When the probability of making a jump tends to zero as an appropriate power of $n$ we prove the existence of a total variation pre-cutoff for this walk. In addition, we show that the process obtained by subsampling our walk at jump times exhibits a true cutoff, with mixing time dependent on whether the step distribution has zero mean.

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Michael E. Bate, Stephen B. Connor. 2014-07-14. Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod $n$. https://arxiv.org/abs/1407.3580

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