USING BERNOULLI MAPS TO ACCELERATE MIXING OF A RANDOM WALK ON THE TORUS

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.