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A hydrodynamic limit of interacting Brownian particles using Skorohod maps

Clayton Barnes
Monday, May 21, 2018 - 2:30pm to 3:30pm
SMI 304

In 2001, Frank Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian (or inert) in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a multi-particle analog using Skorohod maps, and use properties of these maps to characterize the hydrodynamic limit of the system as the number of Brownian particles approaches infinity. Our method gives existence and uniqueness for the resulting nonlinear PDE with free boundary condition. This seems to be the first time Skorohod maps have been used to prove a hydrodynamic limit. As this is also my final exam, I will give a light overview of other results in my thesis which include a strong approximation for the Newtonian particle and a discrete approximation scheme that confirms a conjecture of Burdzy and White (2008).

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