• Corpus ID: 119617292

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

@article{Bernardin2017SlowTF,
  title={Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps},
  author={C'edric Bernardin and Patr{\'i}cia Gonçalves and Byron Oviedo Jimenez},
  journal={arXiv: Probability},
  year={2017}
}

• C. Bernardin, P. Gonçalves, B. Jimenez
• Published 23 February 2017
• Mathematics
• arXiv: Probability

We consider an exclusion process with long jumps in the box $\Lambda_N=\{1, \ldots,N-1\}$, 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.