A functional central limit theorem for the empirical Ripley's K-function

We establish a functional central limit theorem for the empirical Ripley's K-function of Gibbs point processes and point processes with fast decay of correlations. Our theorem greatly extend past results that were restricted to the Poisson case and allow to determine the asymptotic behaviour of statistics based on the K-function which may be used, for example, to develop goodness-of-fit tests. We illustrate this in a simulation study.