Gravitation versus Brownian motion

Sayan Banerjee, Krzysztof Burdzy, Mauricio Duarte

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1531-1565
Number of pages35
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume55
Issue number3
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Brownian motion
  • Gravitation
  • Inert drift
  • Local time
  • Total variation distance

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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