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.