On the expected diameter of planar Brownian motion

James McRedmond, Chang Xu

Research output: Contribution to journalArticle

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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 languageEnglish
Pages (from-to)1-4
Number of pages4
JournalStatistics and Probability Letters
Volume130
Early online date14 Jul 2017
DOIs
Publication statusPublished - 30 Nov 2017

Keywords

  • Brownian motion
  • convex hull
  • diameter

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