A mechanical model of Brownian motion with uniform motion area

Song Liang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We consider a system of plural massive particles interacting with an ideal gas, evolved according to non-random mechanical principles, via interaction potentials. We first prove the weak convergence of the (position, velocity)-process of the massive particles until certain time, under a certain scaling limit, and give the precise expression of the limiting process, a diffusion process. In the second half, we consider a special case which includes the case of "two same type massive particles" as a concrete example, and prove the convergence of the process of the massive particles until any time. The precise description of the limit process, a combination of a "diffusion phase" and a "uniform motion phase", is also given.

Original languageEnglish
Pages (from-to)235-334
Number of pages100
JournalJournal of Mathematical Sciences (Japan)
Issue number2
Publication statusPublished - 2014
Externally publishedYes


  • Brownian motion
  • Convergence
  • Diffusion
  • Infinite particle systems
  • Markov process
  • Non-random mechanics
  • Uniform motion

ASJC Scopus subject areas

  • General Mathematics


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