Self-diffusion for Brownian motions with local interaction. (English) Zbl 0961.60099

The author studies the motion of a tagged particle in a system of interacting Brownian motions on the unit circle in the scaling limit under diffusive scaling. The interaction interpolates between the noninteracting and the totally reflecting case. For bounded initial density profile the limit dynamics is explicitly derived. It is also shown that the motions of two tagged particles become independent in the limit. The derivation of the limit dynamics is based on the approximation of the local interaction time in the corresponding martingale problem.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
82C22 Interacting particle systems in time-dependent statistical mechanics
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