Hydrodynamic limits: The emergence of fractional boundary conditions

Abstract

In these notes, I describe some recent developments concerning the hydrodynamic limit for some stochastic interacting particle systems that have been investigated by a group of researchers working under the research project funded by the ERC Starting Grant no. 715734. The treatment is focused on stochastic systems with an open boundary, for which one can obtain partial differential equations with boundary conditions; or stochastic systems with long-range interactions, for which fractional equations appear in the scaling limits of those models. This is by no means an extensive review about the subject; the topics chosen reflect the personal perspective of the author.