Abstract
We consider a birth and growth process with germs being born according to a Poisson point process 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 geometrical shape of free crystals, we prove that the random field is mixing in the sense of ergodic theory, and we also obtain estimates for the absolute regularity coefficient. To cite this article: Y. Davydov, A. Illig, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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