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# Probability Seminar: James Nolan, Duke University

## April 5, 2018 @ 4:15 pm - 5:15 pm

**Probability Seminar
**

**Thursday, April 5, 2018**

Hanes 125

4:15 PM

Hanes 125

4:15 PM

**James Nolan
**

**Mathematics Department**

Duke University

Duke University

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.

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**Refreshments will be served at 3:45 in the 3rd floor lounge of Hanes Hall**