A Mechanical Model of Brownian Motion with Uniform Motion Area
Vol. 21 (2014), No. 2, Page 235–334.
Liang, Song
A Mechanical Model of Brownian Motion with Uniform Motion Area
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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.
Keywords: Infinite particle systems, non-random mechanics, Markov process, diffusion, convergence, Brownian motion, uniform motion.
Mathematics Subject Classification (2010): Primary 70F45; Secondary 34F05, 60B10.
Mathematical Reviews Number: MR3288810
Received: 2013-10-21
