Diffusive fluctuations of long-range symmetric exclusion with a slow barrier.

In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in Z with long jumps. The transition probability of the jump from x to y is proportional to | x − y | − γ − 1. Here we restrict to the choice γ ≥ 2 so that the system has a diffusive behaviour. Moreover, when particles move between negative integers sites and sites in N , the jump rates are slowed down by a factor α n − β , where α > 0 , β ≥ 0 and n is the scaling parameter. Depending on the values of β and γ , we obtain several stochastic partial differential equations, corresponding to a heat equation without boundary conditions, or with Robin boundary conditions or Neumann boundary conditions. [ABSTRACT FROM AUTHOR]