English

Gravitation versus Brownian motion

Probability 2017-02-24 v3

Abstract

We investigate the motion of an inert (massive) particle being impinged from below by a particle performing (reflected) Brownian motion. The velocity of the inert particle increases in proportion to the local time of collisions and decreases according to a constant downward gravitational acceleration. We study fluctuations and strong laws of the motion of the particles. We further show that the joint distribution of the velocity of the inert particle and the gap between the two particles converges in total variation distance to a stationary distribution which has an explicit product form.

Keywords

Cite

@article{arxiv.1510.02328,
  title  = {Gravitation versus Brownian motion},
  author = {Sayan Banerjee and Krzysztof Burdzy and Mauricio Duarte},
  journal= {arXiv preprint arXiv:1510.02328},
  year   = {2017}
}

Comments

Overall presentation improved. 44 pages

R2 v1 2026-06-22T11:15:44.913Z