## A Mechanical Model of Brownian Motion with Uniform Motion Area

J. Math. Sci. Univ. Tokyo
Vol. 21 (2014), No. 2, Page 235–334.

Liang, Song
A Mechanical Model of Brownian Motion with Uniform Motion Area
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.