On the expected diameter of planar Brownian motion

McRedmond, James and Xu, Chang (2017) On the expected diameter of planar Brownian motion. Statistics and Probability Letters, 130. pp. 1-4. ISSN 0167-7152 (https://doi.org/10.1016/j.spl.2017.07.001)

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Abstract

Known results show that the diameter d1 of the trace of planar Brownian motion run for unit time satisfies 1.595 ≤ Ed1 ≤ 2.507. This note improves these bounds to 1.601 ≤ Ed1 ≤ 2.355. Simulations suggest that Ed1 ≈ 1.99.

ORCID iDs

McRedmond, James and Xu, Chang ORCID logoORCID: https://orcid.org/0000-0003-2674-0034;
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