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

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Abstract

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.

Original languageEnglish
Pages (from-to)203-235
Number of pages33
JournalRandom Operators and Stochastic Equations
Volume29
Issue number3
DOIs
Publication statusPublished - 2021 Sep 1

Keywords

  • Infinite particle systems
  • classical mechanics
  • diffusions

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability

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