16.04.2019 um 12:00 Uhr in Raum 69/E15
Ronan Herry (Universität Bonn)
Stable approximation on the Poisson space
We prove a stable limit theorem for functionals of a Poisson point process. The limit can be taken in the class of conditionally Gaussian distributions. Our work generalizes the recently established fourth moment theorem on the Poisson space (Döbler & Peccati, 2018 <tel:2018>). We will present applications to the study of some stochastic processes.
The proof relies on stochastic analysis and Malliavin calculus for the Poisson space. I will review all the definitions and important results on the subject.
If time permits, I will also hint at some potential applications in stochastic geometry (still under investigation).
30.04.2019 um 12:00 Uhr in Raum 69/E15
Random Spatial Networks
07.05.2019 um 10:30 Uhr in Raum 69/E15
Grace Itunuoluwa Akinwande
Poisson approximations for a random f-vector
We consider the f-vector of a random simplicial complex in the sparse regime and get bounds fot the Poisson approximation in the univariate case.
14.05.2019 um 12:00 Uhr in Raum 69/E15
Binh Hong Ngoc
Lattice point covering problem
We discuss some results for lattice point covering problems in dimension two and give bounds for the expected mean width of randomized lattice polygons.
21.05.2019 um 12:00 Uhr in Raum 69/E15
High Dimensional Random Simplices
28.05.2019 um 14:00 Uhr in Raum 69/118
CLTs for Geometric Functionals of Compact Sets
We consider a Boolean model based on an inhomogenous Poisson process of compact particles in Euclidean space. Our approach builds on the work of Hug, Last and Schulte (2016) and adapts their results to be compatible with our setting. We look at applications in network science, where aforementioned compact sets model communication ranges of wireless network participants.
11.06.2019 um 12:00 Uhr in Raum 69/E15
Curse Of Dimensionality: Limit Theorems to Infinity and beyond
We start with a short introduction to high-dimensional limit theorems for edge-counting statistics in the random geometric graph concerning the difficulties compared to fixed-dimension limit theorems in general. Afterwards we investigate a model for complete-subgraph counts in the Gilbert Graph with respect to the supremum-norm and the actual state of my research on this topic. Finally we raise the question, if the approach holds for a certain class of metrics on the d-dimensional real space, when d tends to infinity.