Worst-case mixing estimates for Brownian motion with semipermeable barriers

Alexander Van Werde; Jaron Sanders

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arXiv · 2512.02661

Worst-case mixing estimates for Brownian motion with semipermeable barriers

Alexander Van Werde·Jaron Sanders

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Abstract

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.

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Alexander Van Werde, Jaron Sanders. 2025-12-02. Worst-case mixing estimates for Brownian motion with semipermeable barriers. https://arxiv.org/abs/2512.02661

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