3 papers
math.PR2018
Functional limit theorems for random walks
Chak Hei Lo, James McRedmond, Clare Wallace
We survey some geometrical properties of trajectories of -dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numb…
math.PR2018
The convex hull of a planar random walk: perimeter, diameter, and shape
James McRedmond, Andrew R. Wade
We study the convex hull of the first steps of a planar random walk, and present large- asymptotic results on its perimeter length , diameter , and shape. In the c…
math.PR2017
On the expected diameter of planar Brownian motion
James McRedmond, Chang Xu
Known results show that the diameter of the trace of planar Brownian motion run for unit time satisfies . This note improves these bound…