Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion

Frank Aurzada; Martin Kolb; Dominic T. Schickentanz

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arXiv · 2308.04866

Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion

Frank Aurzada·Martin Kolb·Dominic T. Schickentanz

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Abstract

We show that a Brownian motion on $\mathbb{R}_{\ge 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This can be seen as an extreme example of entropic repulsion. Moreover, we explicitly determine the exact asymptotic behaviour of the probability that a Brownian motion on $[0,T]$ spends limited time outside a bounded interval, as $T \to \infty$.

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Frank Aurzada, Martin Kolb, Dominic T. Schickentanz. 2023-08-09. Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion. https://arxiv.org/abs/2308.04866

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