TY - JOUR

T1 - A mechanical model of Brownian motion with uniform motion area

AU - Liang, Song

N1 - Publisher Copyright:
© 2014, University of Tokyo. All rights reserved.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Brownian motion

KW - Convergence

KW - Diffusion

KW - Infinite particle systems

KW - Markov process

KW - Non-random mechanics

KW - Uniform motion

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M3 - Article

AN - SCOPUS:84925441979

VL - 21

SP - 235

EP - 334

JO - Journal of Mathematical Sciences (Japan)

JF - Journal of Mathematical Sciences (Japan)

SN - 1340-5705

IS - 2

ER -