Using Bernoulli maps to accelerate mixing of a random walk on the torus

2023/03/06 by Iyer, Gautam, Lu, Ethan, Nolen, James · 1 citation
#60J05 (Primary) 37A25 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2303.03528

Abstract

We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mixing time of the random walk alone is O(1/ε²), where ε is the step size. Our main results show that for a class of Bernoulli maps, when the random walk is alternated with the Bernoulli map φ the mixing time becomes O(|ln ε|). We also study the dissipation time of this process, and obtain O(|ln ε|) upper and lower bounds with explicit constants.

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• Exponentially mixing flows with slow enhanced dissipation

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