Affiliation:
1. School of Education , Waseda University , Tokyo , Japan
Abstract
Abstract
We provide a connection between Brownian motion and a classical Newton mechanical system
in dimension
d
≥
3
{d\geq 3}
.
This paper is an extension of
[S. Liang,
A mechanical model of Brownian motion for one massive particle including slow light particles,
J. Stat. Phys. 170 2018, 2, 286–350].
Precisely, we consider a system of one massive particle interacting with an ideal gas,
evolved according to non-random Newton mechanical principles, via interaction potentials,
without any assumption requiring that the initial energies of the environmental particles should be
restricted to be “high enough”.
We prove that, as in the high-dimensional case,
the position/velocity process of the massive particle converges to a diffusion process
when the mass of the environmental particles converges to 0,
while the density and the velocities of them go to infinity.
Subject
Statistics and Probability,Analysis