Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of the mean value of functional $p$-norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we...

We study average topological summaries of Vietoris–Rips complexes built on top of random point clouds in the D-dimensional Euclidian space in two setups: i) a homogeneous Poisson point process (HPPP) with intensity n and ii) N i.i.d. points sampled from a uniform elliptical distribution. In...