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

IF 0.3 Q4 STATISTICS & PROBABILITY Random Operators and Stochastic Equations Pub Date : 2021-07-31 DOI:10.1515/rose-2021-2062
Song Liang
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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.
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d≥3的一个包含低能轻粒子的大质量粒子的布朗运动力学模型
摘要我们给出了布朗运动与维数d≥3的经典牛顿力学系统之间的联系。本文是[S.Lang,一个包括慢光粒子的大质量粒子布朗运动的力学模型,J.Stat.Phys.170 2018,2286-350]的扩展。准确地说,我们考虑的是一个由一个大质量粒子与理想气体相互作用的系统,该系统根据非随机牛顿力学原理,通过相互作用势演化而来,而没有任何假设要求环境粒子的初始能量应被限制为“足够高”。我们证明,与高维情况一样,当环境粒子的质量收敛到0时,大质量粒子的位置/速度过程收敛到扩散过程,而它们的密度和速度则无穷大。
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来源期刊
Random Operators and Stochastic Equations
Random Operators and Stochastic Equations STATISTICS & PROBABILITY-
CiteScore
0.60
自引率
25.00%
发文量
24
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