A classical mechanical model of Brownian motion with plural particles

Shigeo Kusuoka; Song Liang

doi:10.1142/S0129055X10004077

A classical mechanical model of Brownian motion with plural particles

Shigeo Kusuoka^*, Song Liang

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

We give a connection between diffusion processes and classical mechanical systems in this paper. Precisely, we consider a system of plural massive particles interacting with an ideal gas, evolved according to classical mechanical principles, via interaction potentials. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit, and give the precise expression of the limiting process, a diffusion process.

Original language	English
Pages (from-to)	733-838
Number of pages	106
Journal	Reviews in Mathematical Physics
Volume	22
Issue number	7
DOIs	https://doi.org/10.1142/S0129055X10004077
Publication status	Published - 2010 Aug
Externally published	Yes

Keywords

Brownian motion
Infinite particle systems
Markov processes
classical mechanics
convergence
diffusions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1142/S0129055X10004077

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title = "A classical mechanical model of Brownian motion with plural particles",

abstract = "We give a connection between diffusion processes and classical mechanical systems in this paper. Precisely, we consider a system of plural massive particles interacting with an ideal gas, evolved according to classical mechanical principles, via interaction potentials. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit, and give the precise expression of the limiting process, a diffusion process.",

keywords = "Brownian motion, Infinite particle systems, Markov processes, classical mechanics, convergence, diffusions",

author = "Shigeo Kusuoka and Song Liang",

note = "Funding Information: We would like to thank the referees for their valuable comments which helped to improve the manuscript in many ways. Also we would like to thank Professor Sergio Albeverio for read the manuscript carefully. This work was financially supported by Grant-in-Aid for the Encouragement of Young Scientists (No. 21740063), Japan Society for the Promotion of Science.",

year = "2010",

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doi = "10.1142/S0129055X10004077",

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T1 - A classical mechanical model of Brownian motion with plural particles

AU - Kusuoka, Shigeo

AU - Liang, Song

N1 - Funding Information: We would like to thank the referees for their valuable comments which helped to improve the manuscript in many ways. Also we would like to thank Professor Sergio Albeverio for read the manuscript carefully. This work was financially supported by Grant-in-Aid for the Encouragement of Young Scientists (No. 21740063), Japan Society for the Promotion of Science.

PY - 2010/8

Y1 - 2010/8

N2 - We give a connection between diffusion processes and classical mechanical systems in this paper. Precisely, we consider a system of plural massive particles interacting with an ideal gas, evolved according to classical mechanical principles, via interaction potentials. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit, and give the precise expression of the limiting process, a diffusion process.

AB - We give a connection between diffusion processes and classical mechanical systems in this paper. Precisely, we consider a system of plural massive particles interacting with an ideal gas, evolved according to classical mechanical principles, via interaction potentials. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit, and give the precise expression of the limiting process, a diffusion process.

KW - Brownian motion

KW - Infinite particle systems

KW - Markov processes

KW - classical mechanics

KW - convergence

KW - diffusions

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EP - 838

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 7

ER -

A classical mechanical model of Brownian motion with plural particles

Abstract

Keywords

ASJC Scopus subject areas

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