Worst-case mixing estimates for Brownian motion with semipermeable barriers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909940277313536 |
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| author | Van Werde, Alexander Sanders, Jaron |
| author_facet | Van Werde, Alexander Sanders, Jaron |
| contents | We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar domain and that the barriers are one-dimensional closed curves. We establish an upper bound on the mixing time and a lower bound on the stationary distribution in terms of geometric parameters. These worst-case bounds decay at an exponential rate as the domain grows large, and we give examples that show that exponential decay is necessary in our worst-case setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Worst-case mixing estimates for Brownian motion with semipermeable barriers Van Werde, Alexander Sanders, Jaron Probability 37A25, 60J65, 60H10 We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar domain and that the barriers are one-dimensional closed curves. We establish an upper bound on the mixing time and a lower bound on the stationary distribution in terms of geometric parameters. These worst-case bounds decay at an exponential rate as the domain grows large, and we give examples that show that exponential decay is necessary in our worst-case setting. |
| title | Worst-case mixing estimates for Brownian motion with semipermeable barriers |
| topic | Probability 37A25, 60J65, 60H10 |
| url | https://arxiv.org/abs/2512.02661 |