Limit theory for spatial random networks

Spatial random networks are an integral part of our daily lives. Such networks, characterized by intricate spatial arrangements of nodes and edges, serve as powerful models for understanding complex systems ranging from social networks, infrastructure networks, the power grid or even neural networks. Embedded within these networks often lie crucial functionalities. Thus, modeling such networks is of great interest to gain insights into their intrinsic behavior. In topological data analysis, random point clouds are used to build such models and connections are determined by following certain rules, therefore, creating a random spatial network. This thesis is concerned with limit theory for spatial random networks. In particular, we study the behavior in rare events. Our work yields large deviations principles, normal and Poisson approximation for functionals of certain spatial random networks.