Derivation of an Ornstein-Uhlenbeck Process for a Massive Particle in a Rarified Gas of Particles

作者：Bodineau Thierry^*; Gallagher Isabelle; Saint Raymond Laure

来源：Annales Henri Poincare, 2018, 19(6): 1647-1709.

DOI：10.1007/s00023-018-0674-6

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 (Lecture notes in physics, vol 38, Springer, New York, pp 1-111, 1975) together with the pruning procedure from Bodineau et al. (Invent Math 203(2):493-553, 2016) 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.

• 出版日期2018-6