Statistics and Data Science Seminar
Prof. Elton P Hsu
Northwestern University
How fast does a Brownian motion move on a manifold?
Abstract: How fast does a transient Brownian motion escape to infinity is an interesting question. For example, it is well known that Brownian motion in a euclidean
space of dimension 3 and higher escapes to infinity at approximately the rate of the square root of time. Which geometric quantity controls the rate of escape
is an interesting question. We will explain that the speed of Brownian motion can be effectively controlled by the volume growth rate of a complete Riemannian manifold. A precise integral
criterion is obtained which in many cases is sharp.
Wednesday November 12, 2008 at 4:15 PM in SEO 612