A classical mechanical model of Brownian motion with plural particles

Shigeo Kusuoka*, Song Liang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 languageEnglish
Pages (from-to)733-838
Number of pages106
JournalReviews in Mathematical Physics
Issue number7
Publication statusPublished - 2010 Aug
Externally publishedYes


  • 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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