Event Type:

Probability Seminar

Date/Time:

Tuesday, October 25, 2011 - 09:00

Location:

WNGR 201

Guest Speaker:

Institution:

University of Oregon

Abstract:

I will discuss monotonicity properties of Neumann heat kernels. I will prove that the probability of return to a starting point for the radial part of Brownian motion (Bessel process) is increasing when the point moves toward the boundary. This is plausible since the boundary reflects the process back toward the starting point. Surprisingly, this result holds only for dimensions 3 and higher. The proof involves "polar" random walk approximation for Brownian motion.