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Spatial random graphs provide an important framework for the analysis of relations and interactions in networks. In particular, the random geometric graph has been intensively studied and applied in various frameworks like network modeling or percolation theory.
In this talk we focus on approximation results for a generalization of the random geometric graph that consists of vertices given by a Gibbs process and (conditionally) independent edges generated from a connection function. Using Stein’s method, we compare this graph model with general spatial random graphs with respect to general integral probability metrics, providing concrete rates in the case of a suitable Wasserstein distance. We then briefly present an application of our results in the context of differential privacy. Finally, we describe how associated kernel Stein discrepancies can be used for goodness-of-fit testing in the framework of point processes and, as future work, spatial random graphs.
