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Brownian motion with inert drift, but without flux: A model |
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| Authors: | Krzysztof Burdzy Robert Ho?yst ?ukasz Pruski |
| Affiliation: | a Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98115-4350, USA b Institute of Physical Chemistry PAS, Dept. III, Kasprzaka 44/52, 01224 Warsaw, Poland c WMP-SN? UKSW, Dewajtis 5, Warsaw, Poland d Department of Mathematics and Computer Science, University of San Diego, 5998 Alcala Park, San Diego, CA 92110-2492, USA |
| Abstract: | We study the motion of a Brownian particle which interacts with a stationary obstacle in two dimensions. The Brownian particle acquires drift proportionally to the time spent on the boundary of the obstacle. The system approaches equilibrium, and the equilibrium distribution for the location and drift magnitude has the product form. The distribution for the location is uniform, while the drift distribution depends on the shape of the obstacle, resembling a gamma function for the circular or elliptic obstacle. |
| Keywords: | Brownian motion drift Flux Equilibrium distribution |
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