Gaussian approximation for sums of region-stabilizing scores

We consider the Gaussian approximation for functionals of a Poisson process that are expressible as sums region-stabilizing (determined by points within some specified regions) score functions and provide bound on rate convergence in Wasserstein Kolmogorov distances. While such results have previously been shown Lachièze-Rey, Schulte Yukich (2019), we extend applicability relaxing conditions assumed there further insight into results. This is achieved working with stabilization regions may differ from balls random radii commonly used literature concerning stabilizing functionals. also allow non-diffuse intensity measures unbounded scores, which useful applications. As our main application, number minimal homogeneous [0,1]dwith d≥2, presumably optimal convergence.