Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U-statistics

Abstract

Continuing the analysis initiated in Lachiéze-Rey and Peccati (2011), we use contraction operators to study the normal approximation of random variables having the form of a U-statistic written on the points in the support of a random Poisson measure. Applications are provided: to boolean models, and coverage of random networks.

References in corpus (8)

• Central limit theorems for $U$-statistics of Poisson point processes
• Gaussian limits for random measures in geometric probability
• Central limit theorems for double Poisson integrals
• The Chen-Stein method for Poisson functionals
• Malliavin-Stein method for multi-dimensional U-statistics of Poisson point processes
• Exact and asymptotic results for intrinsic volumes of Poisson k-flat processes
• The scaling limit of Poisson-driven order statistics with applications in geometric probability
• A Central Limit Theorem for the Poisson-Voronoi Approximation

Cited by in corpus (1)

• Central limit theorems for $U$-statistics of Poisson point processes