@article{0e704fa97c2844bdbf1fae0de5da1730,
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",
month = aug,
doi = "10.1142/S0129055X10004077",
language = "English",
volume = "22",
pages = "733--838",
journal = "Reviews in Mathematical Physics",
issn = "0129-055X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "7",
}