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On the expected diameter of planar Brownian motion.

McRedmond, James and Xu, Chang (2017) 'On the expected diameter of planar Brownian motion.', Statistics & probability letters., 130 . pp. 1-4.


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.

Item Type:Article
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Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:06 July 2017
Date deposited:11 August 2017
Date of first online publication:14 July 2017
Date first made open access:14 July 2018

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