We review a collection of models of random simplicial complexes together with some of the
most exciting phenomena related to them. We do not attempt to cover all existing models …

In this paper we introduce and study a higher dimensional analogue of the giant component
in continuum percolation. Using the language of algebraic topology, we define the notion of …

The persistent Betti numbers are used in topological data analysis (TDA) to infer the scales
at which topological features appear and disappear in the filtration of a topological space …

In this review, the state-of-the-art for goodness-of-fit testing for spatial point processes is
summarized. Test statistics based on classical functional summary statistics and recent …

We study the geometric and topological features of U-statistics of order k when the k-tuples
satisfying geometric and topological constraints do not occur frequently. Using appropriate …

We establish a functional central limit theorem for the empirical Ripley's K-function of Gibbs
point processes and point processes with fast decay of correlations. Our theorem greatly …

This paper adopts a tool from computational topology, the Euler characteristic curve (ECC)
of a sample, to perform one-and two-sample goodness of fit tests. We call our procedure …

We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Čech
filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical …

A flexible approach for normal approximation of geometric and topological statistics Page 1
Bernoulli 30(4), 2024, 3029–3058 https://doi.org/10.3150/23-BEJ1705 A flexible approach for …

To recover the topology of a manifold in the presence of heavy tailed or exponentially
decaying noise, one must understand the behavior of geometric complexes whose points lie …