Sala Seminari (Dip. Matematica).
Interacting particle systems is a recently developed field in the theory of Markov processes with many applications: particle systems have been used to model phenomena ranging from traffic behaviour to spread of infection and tumour growth. We introduce this field through the study of the simple exclusion process. We will construct the generator of this process and we will give a convergence result of the spatial particle density to the solution of the heat equation. We will also discuss a variation of the simple exclusion process with proliferation.