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May 2018 Mixing time and cutoff for a random walk on the ring of integers mod $n$
Michael Bate, Stephen Connor
Bernoulli 24(2): 993-1009 (May 2018). DOI: 10.3150/16-BEJ832

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 Bate. Stephen Connor. "Mixing time and cutoff for a random walk on the ring of integers mod $n$." Bernoulli 24 (2) 993 - 1009, May 2018. https://doi.org/10.3150/16-BEJ832

Information

Received: 1 December 2015; Revised: 1 February 2016; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778355
MathSciNet: MR3706784
Digital Object Identifier: 10.3150/16-BEJ832

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 2 • May 2018
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