TY - JOUR

T1 - A mechanical model of Brownian motion for one massive particle including low energy light particles in dimension d ≥ 3

AU - Liang, Song

N1 - Publisher Copyright:
© 2021 Walter de Gruyter GmbH, Berlin/Boston.

PY - 2021/9/1

Y1 - 2021/9/1

N2 - We provide a connection between Brownian motion and a classical Newton mechanical system in dimension d ≥ 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.

AB - We provide a connection between Brownian motion and a classical Newton mechanical system in dimension d ≥ 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.

KW - Infinite particle systems

KW - classical mechanics

KW - diffusions

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U2 - 10.1515/rose-2021-2062

DO - 10.1515/rose-2021-2062

M3 - Article

AN - SCOPUS:85112286989

VL - 29

SP - 203

EP - 235

JO - Random Operators and Stochastic Equations

JF - Random Operators and Stochastic Equations

SN - 0926-6364

IS - 3

ER -