Studies in Nonequilibrium Behaviors of Tagged Particles

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The proposed project is to study some asymptotic fluctuations of a distinguished, or tagged particle interacting with others in certain models of simple exclusion and zero-range particle systems. The physical feeling is that the tagged particle is in some scale a type of homogenized random walk or Brownian motion with parameters reflecting system interactions. This picture to first order in terms of the law of averages has been established. Also, to some extent, under equilibrium conditions, second order features such as "fluctuations" have been understood. But less is known in "non-equilibrium" situations. In this context, the specific proposed work is to characterize the non-equilibrium fluctuations in certain "mean-zero" simple exclusion and zero-range systems where some calculation is possible. Resolution of these issues will also have some bearing on non-equilibrium fluctuations of "hydrodynamic limits" which is as well an open problem.Informally, the proposed project is to investigate some asymptotic behaviors of a distinguished, or tagged component interacting with others in certain models of traffic, queuing and fluids. More specifically, the proposed work is to study "non-equilibrium" fluctuations of such tagged components. The broader impacts of the proposal are in its connections with statistical physics where determining tagged component behavior is important to understanding "transport," and "multi-scale" phenomena.