Gravitation versus Brownian motion

Sayan Banerjee; Krzysztof Burdzy; Mauricio Duarte

doi:10.1214/18-AIHP927

Gravitation versus Brownian motion

Sayan Banerjee, Krzysztof Burdzy, Mauricio Duarte

Research output: Contribution to journal › Article › peer-review

4 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 language	English
Pages (from-to)	1531-1565
Number of pages	35
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	55
Issue number	3
DOIs	https://doi.org/10.1214/18-AIHP927
Publication status	Published - 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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10.1214/18-AIHP927

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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 = "Brownian motion, Gravitation, Inert drift, Local time, Total variation distance",

author = "Sayan Banerjee and Krzysztof Burdzy and Mauricio Duarte",

note = "Funding Information: We are grateful to Amarjit Budhiraja and Ruth Williams for very helpful advice. S.B. gratefully acknowledges support from EPSRC Research Grant EP/K013939. K.B.{\textquoteright}s research was supported in part by Simons Foundation Grant 506732. M.D. thanks the support from Nucleo Milenio NC 130062, and FONDECYT grant 11160591. We are also grateful to an anonymous referee whose suggestions greatly improved this article. Publisher Copyright: {\textcopyright} 2019 Association des Publications de l'Institut Henri Poincar{\'e}.",

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AU - Burdzy, Krzysztof

AU - Duarte, Mauricio

N1 - Funding Information: We are grateful to Amarjit Budhiraja and Ruth Williams for very helpful advice. S.B. gratefully acknowledges support from EPSRC Research Grant EP/K013939. K.B.’s research was supported in part by Simons Foundation Grant 506732. M.D. thanks the support from Nucleo Milenio NC 130062, and FONDECYT grant 11160591. We are also grateful to an anonymous referee whose suggestions greatly improved this article. Publisher Copyright: © 2019 Association des Publications de l'Institut Henri Poincaré.

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N2 - 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.

AB - 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.

KW - Brownian motion

KW - Gravitation

KW - Inert drift

KW - Local time

KW - Total variation distance

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JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

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ER -

Gravitation versus Brownian motion

Abstract

Keywords

ASJC Scopus subject areas

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