Mixing properties of crystallization processes

Abstract

We are interested here in a birth-and-growth process where germs are born according to a Poisson point process with intensity measure invariant under space translations. The germs can be born in free space and then start growing until occupying the available space. In order to consider various ways of growing, we describe the crystals at each time through their geometrical properties. In this general framework, the crystallization process can be characterized by the random field giving for a point in the state space the first time this point is reached by a crystal. We prove under general conditions that this random field is mixing in the sense of ergodic theory and obtain estimates for the coefficient of absolute regularity.