Hauptinhalt
Topinformationen
Wochenprogramm
Kolloquium
11.12.2019 um 16:15 Uhr (!) in 69/125
Prof. Dr. Heidemarie Bräsel (Otto-von-Guericke-Universität Magdeburg)
Ethnomathematik – Geometrie auf drei Kontinenten
18.12.2019 um 17:15 Uhr in 69/125
Prof. Dr. Leif Döring (Universität Mannheim)
Stochastic Differential Equations with Jumps - What, Why and How?
Oberseminar Angewandte Analysis
Oberseminar Stochastik
17.12.2019 um 12:00 Uhr in Raum 69/E15
Jens Grygierek
Random Geometric Structures
In the first part, we use a stationary Poisson point process to construct two random simplicial complexes, the random Vietoris-Rips complex and the random Cech complex, that are rich enough to realize any compact topological manifold, at least up to homotopy equivalence.
In the second part, we investigate the random Vietoris-Rips complex constructed from a stationary Poisson point process on a d-dimensional compact set using the uniform norm.
Opposed to most of the existing literature in which the focus lies on random geometric graphs in the fixed dimensional case, we will generalize this model by investigating the asymptotic distributional behavior of the f-vector if the intensity as well as the space dimension d tend to infinity simultaneously.
It turns out, that the phase-transition phenomenon occurs also in the components of the f-vector of the random Vietoris-Rips complex in the fixed and high-dimensional cases.
