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Hydrodynamical behavior for the generalized symmetric exclusion with open boundary
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abstract
We analyze the generalized symmetric exclusion process, which allows at most $\alpha$ particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter $\theta\in\mathbb R$. We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of $\theta$, the equation is supplemented with different boundary conditions. Setting $\alpha = 1$ we find the results known in [1] for the symmetric simple exclusion process.
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Derivation of non-polynomial fractional diffusions from the generalized exclusion with a slow barrier
The hydrodynamic limit of a generalized exclusion process with long jumps and a slow barrier is ∂tρ = L^γ_κ F(ρ), with F any convergent power series on [0,Ne].
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