Approaches to asymptotics for U-statistics of Gibbs facet processes

Abstract

It is shown how the central limit theorem for U-statistics of spatial Poisson point processes can help to derive the central limit theorem for U-statistics of a Gibbs facet process from stochastic geometry. A full-dimensional submodel enables a simpler approach to its investigation.

Finally the general situation is studied and the asymptotics with increasing intensity'is described.

Keywords

• Central limit theorem
• Gibbs facet process
• U-statistics