Abstract:

The symmetric inclusion process (SIP) is an interacting particle system discovered as the dual process of a Markov diffusion that conserves the total energy, it can be tough as the inclusion counterpart of the well-known exclusion process. In this talk, I will present the model with an open boundary, i.e. with two reservoirs which create a flux of particles in the bulk putting the model in a non-equilibrium setting. We will see that via the duality property, we can characterize some correlations of its stationary measure in non-equilibrium and we will also see what are, in this open setting, the so-called hydrodynamic and hydrostatic limit.