Central limit theorem for Gibbsian U-statistics of facet processes

2015/04/14 by Jakub Vecera, Vecera, Jakub
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1504.03589

15 pages

arxiv created 2015/10/05 · arxiv updated 2015/10/06

Abstract

Special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic moments for interaction U-statistics are calculated and using the method of moments the central limit theorem is derived.

Related

• Approaches to asymptotics for U-statistics of Gibbs facet processes
• Interaction processes for unions of facets, a limit behavior
• Functionals of spatial point processes having a density with respect to the Poisson process
• Bounds for the probability generating functional of a Gibbs point process
• Central limit theorems and asymptotic independence for local U-statistics on diverging halfspaces