Using Bernoulli maps to accelerate mixing of a random walk on the torus
| Autor: | Iyer, Gautam, Lu, Ethan, Nolen, James |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $O(1/\epsilon^2)$, where $\epsilon$ 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 $\varphi$ the mixing time becomes $O(|\ln \epsilon|)$. We also study the \emph{dissipation time} of this process, and obtain $O(|\ln \epsilon|)$ upper and lower bounds with explicit constants. Comment: 31 pages, 2 figures |
| Databáze: | arXiv |
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