1 citations · 1 across the 3 of their papers we have counts for
5 papers
Poisson and Gaussian fluctuations for the -vector of high-dimensional random simplicial complexes
Jens Grygierek
We investigate the high-dimensional asymptotic distributional behavior of the -vector of a random Vietoris-Rips complex, that is generated over a stationary Poisson poi…
Poisson fluctuations for edge counts in high-dimensional random geometric graphs
Jens Grygierek
We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method. Our estimates only involve firs…
Multivariate Normal Approximation for functionals of random polytopes
Jens Grygierek
Consider the random polytope, that is given by the convex hull of a Poisson point process on a smooth convex body in . We prove central limit theorems for continuous…
Gigantic random simplicial complexes
Jens Grygierek, Martina Juhnke-Kubitzke, Matthias Reitzner +2
We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalen…
Gaussian fluctuations for edge counts in high-dimensional random geometric graphs
Jens Grygierek, Christoph Thaele
Consider a stationary Poisson point process in and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This cons…