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

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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.