We consider the extension of the Euclidean stochastic geometry Poisson Hail
model to the case where the service speed is zero in some subset of the
Euclidean space and infinity in the complement. We use and develop tools
pertaining to sub-additive ergodic theory in order to establish shape theorems
for the growth of the ice-heap under light tail assumptions on the hailstone
characteristics. The asymptotic shape depends on the statistics of the
hailstones, the intensity of the underlying Poisson point process and on the
geometrical properties of the zero speed set.Comment: Final version accepted in Advances in Applied Probabilit
