A mechanical model of Brownian motion for one massive particle including low energy light particles in dimension d ≥ 3
We provide a connection between Brownian motion and a classical Newton mechanical system in dimension . 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...
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Published in | Random operators and stochastic equations Vol. 29; no. 3; pp. 203 - 235 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Berlin
De Gruyter
01.09.2021
Walter de Gruyter GmbH |
Subjects | |
Online Access | Get full text |
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Summary: | We provide a connection between Brownian motion and a classical Newton mechanical system
in dimension
.
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. |
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ISSN: | 0926-6364 1569-397X |
DOI: | 10.1515/rose-2021-2062 |