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|-gamma -1. Here we restrict to the choice gamma > 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 alpha n-beta, where alpha > 0, beta > 0 and n is the scaling parameter. Depending on the values of beta and gamma, we obtain several stochastic partial differential equations, corresponding to a heat equation without boundary conditions, or with Robin boundary conditions or Neumann boundary conditions.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).