Archimedes' principle for Brownian liquid

Abstract

We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes' principle. The analysis rests on constructing reflecting Brownian motion with drift in a general open connected domain and studying its stationary distribution. In dimension two we utilize known results about sphere packing.

Published in at http://dx.doi.org/10.1214/11-AAP765 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Absolute continuity of symmetric Markov processes
• On pathwise uniqueness for reflecting Brownian motion in $C^{1+\gamma }$ domains

Cited by in corpus (4)

• Phases of granular matter
• Archimedes' principle for ideal gas
• SDE with oblique reflection on domains defined by multiple constraints
• Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect