The self-similar evolution of stationary point processes via persistent homology

Persistent homology provides a robust methodology to infer topological structures from point cloud data. In this talk I will explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point processes. I will introduce measures on the space of persistence diagrams and the self-similar scaling of a one-parameter family of these. As the main result I will discuss a packing relation between the occurring scaling exponents.