Youri Davydov
Ergodic properties of crystallization processes
We are interested in a birth-and-growth process where germs are born according to a Poisson point process with invariant under translation (in space) intensity measure. The germs can be born in free space and then start growing until occupying the available space. In this general framework, the crystallization process can be characterized by the random field giving for a point in the space state the first time this point is reached by a crystal. We prove under general conditions on speed growth and geometrical shape of free crystals that this random field is mixing in the sens of the ergodic theory and obtain estimates for the absolute regularity coefficient.