Search

Features related to the perimeter of the convex hull C n of a random walk in R 2 are studied, with particular attention given to its length L n . Bounds on the variance of L n are obtained to show that, for walks with drift, L n obeys a strong law. Exponential bounds on the tail probabilities of L n under special conditions are also obtained. We then develop simple expressions for the expected values of other features of C n , including the number of faces, the sum of the lengths and squared lengths of the faces, and the number of faces of length t or less