arXiv:1707.03725 Abstract | arXiv Analytics

arXiv:1707.03725 [math.PR]Abstract References Reviews Resources

On the expected diameter of planar Brownian motion

Published 2017-07-12Version 1

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

Comments: 5 pages

Categories: math.PR

Subjects: 60J65, 60D05

Keywords: expected diameter, planar brownian motion run, unit time satisfies, simulations

Related articles: Most relevant | Search more

arXiv:0807.3571 [math.PR] (Published 2008-07-22)

On the expected diameter of an L2-bounded martingale

Lester E. Dubins, David Gilat, Isaac Meilijson

arXiv:math/9508222 [math.PR] (Published 1995-08-02)

The dimension of the Brownian frontier is greater than 1

Christopher J. Bishop, Peter Jones, Robin Pemantle, Yuval Peres

arXiv:1007.3385 [math.PR] (Published 2010-07-20)