On the expected diameter of planar Brownian motion

Abstract

Known results show that the diameter $d_1$ of the trace of planar Brownian motion run for unit time satisfies $1.595\le \mathbb{E}{d}_1\le 2.507$. This note improves these bounds to $1.601\le \mathbb{E}{d}_1\le 2.355$. Simulations suggest that $\mathbb{E}{d}_1\approx 1.99$.

arXiv comment5 pages

References in corpus (1)

• Convex hulls of random walks and their scaling limits

Cited by in corpus (1)

• The convex hull of a planar random walk: perimeter, diameter, and shape