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arXiv · 1707.03725

On the expected diameter of planar Brownian motion

James McRedmond·Chang Xu
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Abstract

Known results show that the diameter $d_1$ of the trace of planar Brownian motion run for unit time satisfies $1.595 \leq \mathbb{E} d_1 \leq 2.507$. This note improves these bounds to $1.601 \leq \mathbb{E} d_1 \leq 2.355$. Simulations suggest that $\mathbb{E} d_1 \approx 1.99$.

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James McRedmond, Chang Xu. 2017-07-12. On the expected diameter of planar Brownian motion. https://doi.org/10.1016/j.spl.2017.07.001

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