Abstract
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 language | English |
---|---|
Pages (from-to) | 235-334 |
Number of pages | 100 |
Journal | Journal of Mathematical Sciences (Japan) |
Volume | 21 |
Issue number | 2 |
Publication status | Published - 2014 |
Externally published | Yes |
Keywords
- Brownian motion
- Convergence
- Diffusion
- Infinite particle systems
- Markov process
- Non-random mechanics
- Uniform motion
ASJC Scopus subject areas
- Mathematics(all)