### 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 |
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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)

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## Cite this

*Journal of Mathematical Sciences (Japan)*,

*21*(2), 235-334.