On the expected diameter of planar Brownian motion

James McRedmond; Chang Xu

doi:10.1016/j.spl.2017.07.001

On the expected diameter of planar Brownian motion

James McRedmond, Chang Xu

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	1-4
Number of pages	4
Journal	Statistics and Probability Letters
Volume	130
Early online date	14 Jul 2017
DOIs	https://doi.org/10.1016/j.spl.2017.07.001
Publication status	Published - 30 Nov 2017

Keywords

Brownian motion
convex hull
diameter

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10.1016/j.spl.2017.07.001

McRedmond-Xu-SPL-2017-On-the-expected-diameter-of-planar-BrownianAccepted author manuscript, 208 KBLicence: CC BY-NC-ND 4.0

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title = "On the expected diameter of planar Brownian motion",

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.",

keywords = "Brownian motion, convex hull, diameter",

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AB - 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.

KW - Brownian motion

KW - convex hull

KW - diameter

UR - https://www.sciencedirect.com/journal/statistics-and-probability-letters

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DO - 10.1016/j.spl.2017.07.001

M3 - Article

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VL - 130

SP - 1

EP - 4

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

On the expected diameter of planar Brownian motion

Abstract

Keywords

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