Advances in Stochastic Duality for Interacting Particle Systems: from many to few

Interacting particle systems (IPS) is a subfield of probability theory that provided a fruitful framework in which several questions of physical interests have been answered with mathematical rigor. An interacting particle system is a stochastic system consisting of a very large number of particles interacting with each other. The class of IPS...

Hydrodynamics for the partial exclusion process in random environment

In this paper, we introduce a random environment for the exclusion process in Z^d obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we...