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

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JournalBernoulli
DateAccepted/In press - 16 Feb 2016
DateE-pub ahead of print - 16 Feb 2016
DatePublished (current) - 2018
Issue number2
Volume24
Pages (from-to)993-1009
Early online date16/02/16
Original languageEnglish

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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© 2017 Bernoulli Society. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

    Research areas

  • math.PR, 60J10

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