On the mean shape of particle processes

Abstract

For a stationary point process X of sets in the convex ring in ℝ d , a relation is given between the mean particles of the section process X ∩ E (where E varies through the set of k-dimensional subspaces in ℝ d ) and a mean particle of X. In particular, it is shown that the mean bodies of all planar sections of X determine the Blaschke body of X and hence the mean normal distribution of X.