Stochastic geometry and stochastic analysis: Poisson U-statistics
Assume that X is a Poisson point process. A Poisson U-statistic with kernel f is the sum of f(x_1,...x_k) over all k-tuples of X. Poisson U-statistics play an important role in Stochastic Geometry. Many functionals of interest can be written as U-statistics. We investigate some elementary properties of Poisson U-statistics, and the limit behaviour of Poisson U-statistics, central limit theorems and concentration inequalities.