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

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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.
Original languageEnglish
Pages (from-to)993-1009
Issue number2
Early online date16 Feb 2016
Publication statusPublished - 2018

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  • math.PR
  • 60J10

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