Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps

Abstract

We consider an exclusion process with long jumps in the box $\Lambda \_N=\{1,\dots ,N-1\}$, for $N\ge 2$, in contact with infinitely extended reservoirs on its left and on its right. The jump rate is described by a transition probability $p(\cdot )$ which is symmetric, with infinite support but with finite variance. The reservoirs add or remove particles with rate proportional to $\kappa N^{-\theta }$, where $\kappa >0$ and $\theta \in \mathbb{R}$. If $\theta >0$ (resp. $\theta <0$) the reservoirs add and fastly remove (resp. slowly remove) particles in the bulk. According to the value of $\theta$ we prove that the time evolution of the spatial density of particles is described by some reaction-diffusion equations with various boundary conditions.

References in corpus (3)

• Exclusion process with slow boundary
• Hydrodynamic limit of particle systems with long jumps
• Scaling properties of the asymmetric exclusion process with long-range hopping

Cited by in corpus (4)

• Diffusive to super-diffusive behavior in boundary driven exclusion
• Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket
• A microscopic model for a one parameter class of fractional laplacians with dirichlet boundary conditions
• Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion