Outputs (2)

The convex hull of a planar random walk: perimeter, diameter, and shape (2018)
Journal Article
McRedmond, J., & Wade, A. R. (2018). The convex hull of a planar random walk: perimeter, diameter, and shape. Electronic Journal of Probability, 23, Article 131. https://doi.org/10.1214/18-ejp257

We study the convex hull of the first n steps of a planar random walk, and present large-n asymptotic results on its perimeter length Ln, diameter Dn, and shape. In the case where the walk has a non-zero mean drift, we show that Ln=Dn ! 2 a.s., and g... Read More about The convex hull of a planar random walk: perimeter, diameter, and shape.

On the expected diameter of planar Brownian motion (2017)
Journal Article
McRedmond, J., & Xu, C. (2017). On the expected diameter of planar Brownian motion. Statistics and Probability Letters, 130, 1-4. https://doi.org/10.1016/j.spl.2017.07.001

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.