We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.
"Bounds for the probability generating functional of a Gibbs point process." Adv. in Appl. Probab. 46 (1) 21 - 34, March 2014. https://doi.org/10.1239/aap/1396360101