Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod n
نویسندگان
چکیده
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 precutoff 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.
منابع مشابه
NO : 19 TITLE : ‘ CUTOFF FOR A RANDOM WALK ON THE INTEGERS MOD n ’ AUTHOR ( S ) : Dr Stephen
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 cutoff for this process, with cutoff time dependent on whether the step distribution has zero mean.
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