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 …

We prove a large deviation principle for the point process associated to k-element
connected components in R d with respect to the connectivity radii rn→∞. The random …

This paper develops the large deviations theory for the point process associated with the
Euclidean volume of $ k $-nearest neighbor balls centered around the points of a …

Let be a sequence of independent random points in with common Lebesgue density f.
Under some conditions on f, we obtain a Poisson limit theorem, as, for the number of large …

Consider a stationary Poisson process in ad-dimensional hyperbolic space. For R> 0 define
the point process ξ R (k) of exceedance heights over a suitable threshold of the hyperbolic …

Poisson approximation of Poisson-driven point processes and extreme values in stochastic
geometry Page 1 Bernoulli 31(1), 2025, 30–54 https://doi.org/10.3150/23-BEJ1688 Poisson …

We study the homology of random Čech complexes generated by a homogeneous Poisson
process. We focus on 'homological connectivity'—the stage where the random complex is …

We discuss a thinning and an embedding procedure to construct finite Gibbs processes with
a given Papangelou intensity. Extending the approach of Hofer-Temmel (Electron. J …

We prove a large deviation principle for the point process of large Poisson $ k $-nearest
neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point …

We establish Poisson and compound Poisson approximations for stabilizing statistics of
$\beta $-mixing point processes and give explicit rates of convergence. Our findings are …