Diffusive to Super-diffusive Behavior in Boundary Driven Exclusion
2022, v.28, Issue 1, 149-178
The purpose of this article is to study the hydrodynamic limit of the symmetric exclusion process with long jumps and in contact with infinitely extended reservoirs for a particular critical regime. The jumps are given in terms of a transition probability that has finite or infinite variance and the hydrodynamic equation is a diffusive equation, in the former case, or a fractional equation, in the latter case. In this work, we treat the critical case, that is, when the variance grows logarithmically with the size of the system and corresponds to the case in which there is a transition from diffusive to super-diffusive behavior.
Keywords: Symmetric exclusion, Hydrodynamic Limit, Boundary conditions, long range interactions