Ergodic properties of crystallization processes

We consider a birth and growth processes with germs being born according to a Poisson point processes whose intensity measure is invariant under translations in space. The germs can be born in unoccupied space and then start growing until they occupy the available space. In this general framework, the crystallization process can be characterized by a random field which, for any point in the state space, assigns the first time at which this point is reached by a crystal. Under general conditions on the growth speed and goemetrical shape of free crystals, we prove that the random field is mixing in the sense of ergodic theory. This result is illustrated by applications to the problem of parameter estimation. Bibl. – 7 titles.