Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: Convex hulls of planar random walks with drift

Presented by Andrew Wade, Durham University

21 January 2013 14:00 in CM221

On each of n unsteady steps, a drunken gardener drops a seed.
Once the flowers have bloomed, what is the minimum length of fencing
required to enclose the garden?
Denote by L(n) the length of the perimeter of the convex hull of n steps
of a planar random walk whose increments have finite second moment and
non-zero mean. Snyder and Steele showed that L(n)/n converges almost
surely to a deterministic limit, and proved an upper bound on the
variance Var[L(n)] = O(n).
I will describe recent work with Chang Xu (Strathclyde) in which we show
that Var[L(n)]/n converges, and give a simple expression for the limit,
which is non-zero for walks outside a certain degenerate class. This
answers a question of Snyder and Steele. Furthermore, we prove a central
limit theorem for L(n) in the non-degenerate case.

Contact i.r.vernon@durham.ac.uk for more information