Probability Seminar: James Nolan, Duke University
Thursday, April 5, 2018
A system of Brownian particles interacting
through a moving reflector
I will describe a system of N particles diffusing on the real line and interacting through a moving boundary. The hydrodymamic limit (N going to infinity) of this system is a solution to a nonlinear free-boundary problem for the heat equation. For finite N, the stochastic system has a stationary distribution, a fact that can be proved using Lyapunov function techniques. An important idea (in analyzing the hydrodynamic limit and the stationary distribution) is averaging at a microscopic scale to produce an effective drift. I will relate this system to some other interacting particle systems which have been studied recently.
Refreshments will be served at 3:45 in the 3rd floor lounge of Hanes Hall