Second-order Characteristics for Stochastic Structures Connected with Gibbs Point Processes†

The points of stationary and isotropic GIBBS point process are marked by exp(corresponding local energy). For the mean mark and two mark product density functions very simple formulae are true which contain the intensity and the pair potential function of the process. Furthermore, there is a close connection between the pair correlation function of the process and the covariance function of the random field given by the conditional intensity.