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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

James Nolan
Mathematics Department
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.

 

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

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Details

Date:
April 5, 2018
Time:
4:15 pm - 5:15 pm
Event Category:

Venue