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Fractional Ficks law for the boundary driven exclusion process with long jumps

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 Added by Cedric Bernardin
 Publication date 2016
  fields Physics
and research's language is English




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A fractional Ficks law and fractional hydrostatics for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities on the left and on the right are derived.

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87 - C. Erignoux , C. Landim , T. Xu 2017
We prove a law of large numbers for the empirical density of one-dimensional, boundary driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary. The proofs rely on duality techniques.
69 - E. Chavez , C. Landim 2015
We consider a one-dimensional, weakly asymmetric, boundary driven exclusion process on the interval $[0,N]cap Z$ in the super-diffusive time scale $N^2 epsilon^{-1}_N$, where $1ll epsilon^{-1}_N ll N^{1/4}$. We assume that the external field and the chemical potentials, which fix the density at the boundaries, evolve smoothly in the macroscopic time scale. We derive an equation which describes the evolution of the density up to the order $epsilon_N$.
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Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.
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