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arXiv · 1710.01610

Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles

Thierry Bodineau·Isabelle Gallagher·Laure Saint-Raymond
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Abstract

We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small deflections. We prove that its velocity is described, in a suitable limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on Lanford's arguments [17] together with the pruning procedure from [3] to reach diffusive times, much larger than the mean free time. Furthermore, we need to introduce a modified dynamics to avoid pathological collisions of atoms with the rigid body: these collisions, due to the geometry of the rigid body, require developing a new type of trajectory analysis.

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Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond. 2017-10-04. Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles. https://doi.org/10.1007/s00023-018-0674-6

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