Hydrostatic limit for the symmetric exclusion process with long jumps: supper-diffusive case

Abstract

Hydrostatic behavior for the one dimensional exclusion process with long jumps in contact 
 with infinite reservoirs at different densities are derived. The jump rate is described by 
 a transition probability $p$ which is proportional to $\vert \cdot\vert ^{-(\gamma +1)}$ for
 $1<\gamma<2$ (super-diffusive case). The reservoirs add or remove particles with rate 
 proportional to $ \kappa>0$.