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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.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.spl.2017.07.001
Publisher statement:© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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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