摘要：We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Čech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth bootstrap of the Euler characteristic and determine its rate of convergence in the Kantorovich-Wasserstein distance and in the Kolmogorov distance.
关键词：60B10; 60D05; 60F05; 62F40; Binomial process; bootstrap; Čech complex; critical regime; Euler characteristics; functional central limit theorem; Normal approximation; Poisson process; Random geometric complexes; smooth bootstrap; Stochastic geometry; topological data analysis; weak convergence
