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A classical mechanical model of Brownian motion with plural particles. (English) Zbl 1372.60096

Summary: We give a connection between diffusion processes and classical mechanical systems in this paper. Precisely, we consider a system of plural massive particles interacting with an ideal gas, evolved according to classical mechanical principles, via interaction potentials. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit, and give the precise expression of the limiting process, a diffusion process.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
34F05 Ordinary differential equations and systems with randomness
60J60 Diffusion processes
60J65 Brownian motion
70F45 The dynamics of infinite particle systems
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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References:

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