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 (3)

• Gaussian limits for random measures in geometric probability
• Central limit theorems for double Poisson integrals
• Exact and asymptotic results for intrinsic volumes of Poisson k-flat processes