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- W2127522182 abstract "In these notes we consider two particle systems: the totally asymmetric simple exclusion process and the totally asymmetric zero-range process. We introduce the notion of hydrodynamic limit and describe the partial differential equation that governs the evolution of the conserved quantity – the density of particles . This equation is a hyperbolic conservation law of type , where the flux F is a concave function. Taking these systems evolving on the Euler time scale tN, a central limit theorem for the empirical measure holds and the temporal evolution of the limit density field is deterministic. By taking the system in a reference frame with constant velocity, the limit density field does not evolve in time. In order to have a non-trivial limit, time needs to be speeded up and for time scales smaller than , there is still no temporal evolution. As a consequence, the current across a characteristic vanishes up to this longer time scale." @default.
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- W2127522182 date "2011-08-01" @default.
- W2127522182 modified "2023-10-18" @default.
- W2127522182 title "A hyperbolic conservation law and particle systems" @default.
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- W2127522182 doi "https://doi.org/10.1080/10236190903382657" @default.
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