Patrick Fitzsimmons, UCSD

Last February, Mike Cranston spoke in this Seminar about a polymer model
based on three-dimensional Brownian motion conditioned to hit (and keep
returning to) the origin. I will discuss the construction and certain
properties of this conditioned Brownian motion from two points of view (i)
Dirichlet forms, and (ii) excursion theory. The latter gives a nice
interpretation of the Johnson-Helms example from martingale theory. It
turns out that this diffusion process is not a semimartingale, even though
its radial part is just a one-dimensional Brownian motion reflected at the
origin.

This is based on joint work with Liping Li of Fudan University.