Ergodic properties of crystallization processes

We consider a birth and growth process with germs which are born according to a Poisson point process whose intensity rneasure is invariant under trunslations of the space. The germs can be born in the unoccupied space; then they grow until they occupy the available space. In this general framework, the crystallization process can be characterized by a random field, which assigns to any point of the state space the first time at which this point is reached by a crigstal. Under general conditions on the growth speed and geometric shape of free crystals, we prone that the random field is mixing in the sense of ergodic theory. This result is illustrated by applications to the problem of parameter estimation. Bibliography: 7 titles.