Angular asymptotics for random walks

Abstract

We study the set of directions asymptotically explored by a spatially homogeneous random walk in $d$-dimensional Euclidean space. We survey some pertinent results of Kesten and Erickson, make some further observations, and present some examples. We also explore links to the asymptotics of one-dimensional projections, and to the growth of the convex hull of the random walk.

arXiv comment24 pages; v2: minor revisions

References in corpus (1)

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