Hydrodynamic Limit for the Symmetric Inclusion Process with Slowly Varying Inhomogeneities

In this thesis we study an interacting particle system: the Symmetric Inclusion Process with slowly varying inhomogeneities (SIP(α)). In the SIP(α) particles display random walk like behaviour subjected to an attractive type of interaction whilst evolving in an inhomogeneous environment. We set out to prove its hydrodynamic limit. The main tool...

Consistent particle systems and duality

We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the Kipnis-Marchioro-Presutti model. Consistent systems are such that the distribution obtained by first evolving n particles and then removing a particle at random is the same as the one...

Exact formulas for two interacting particles and applications in particle systems with duality

We consider two particles performing continuous-time nearest neighbor random walk on Z and interacting with each other when they are at neighboring positions. The interaction is either repulsive (partial exclusion process) or attractive (inclusion process). We provide an exact formula for the Laplace-Fourier transform of the transition...

Hydrodynamic Limit for the Symmetric Inclusion Process

This thesis deals with the proof of the hydrodynamic limit for the symmetric inclusion process (SIP). After introduction of our process and some basic concepts on the theory of Markov processes we proved self-duality for the SIP. Once equipped with SIP self-duality, and together with an assumption on the initial configuration, we were able to...