AG Stochastische Geometrie (Winter Semester 2013/14)
- Lecturer: Prof. Dr. Daniel Hug, Prof. Dr. Günter Last
- Classes: Seminar (0127500)
- Weekly hours: 2
Research seminar of the workgroup Spatial Stochastics and Stochastic Geometry
| Schedule | ||
|---|---|---|
| Seminar: | Friday 9:45-11:15 | Seminarraum K2 |
| Lecturers | ||
|---|---|---|
| Lecturer | Prof. Dr. Daniel Hug | |
| Office hours: Nach Vereinbarung. | ||
| Room 2.051 Kollegiengebäude Mathematik (20.30) | ||
| Email: daniel.hug@kit.edu | Lecturer | Prof. Dr. Günter Last |
| Office hours: by appointment. | ||
| Room 2.001, Sekretariat 2.056 Kollegiengebäude Mathematik (20.30) | ||
| Email: guenter.last@kit.edu | ||
Vorträge
Wenn nicht explizit anders angegeben, finden die Vorträge im Raum K2 (Kronenstr. 32, Eingang ca. 10m links neben der Kaffeebar Schiller) statt.
Freitag, 22.11.2013
9.45 Uhr Matthias Schulte:
Normal approximation on Poisson spaces: Mehler formula, second order Poincare inequality and stabilization
Freitag, 08.11.2013
9.45 Uhr Nicolas Chenavier (Universität Rouen):
A general study of extremes of stationary tessellations and its applications
Abstract: Let and
be a stationary random tessellation and a functional defined on the set of convex bodies. Given a bounded subset
, we investigate the order statistics of
over all cells
with nucleus in
when
. Under suitable conditions, we show that the knowledge of the distribution tail of
, where
is the typical cell, is enough to obtain the convergence of the order statistics and of the underlying point process. The proof is deduced from a Poisson approximation on a dependency graph via
the Chen-Stein method. Several applications are derived in the particular setting of Poisson-Voronoi and Poisson-Delaunay tessellations.
Freitag, 15.11.2013
9.45 Uhr Benjamin Nehring (Ruhr-Universität Bochum):
Construction of Point Processes in Statistical Mechanics
Abstract: We propose a construction of point processes via the method of
cluster expansion. Examples are the classical Gibbs point processes,
where the interaction is given by a stable and regular pair potential as
well as permanental and determinantal point processes. In a second step
we show how to obtain the existence of Gibbs perturbations of the
aforementioned class of point processes.
Freitag, 25.10.2013
9.45 Uhr Anne Marie Svane und Matthias Schulte:
Betti Zahlen zufälliger simplizialer Komplexe - eine Einführung
Freitag, 20.12.2013
9.45 Uhr Julia Hörrmann:
Rekonstruktion konvexer Körper aus Volumentensoren
Freitag, 10.01.2014
9.45 Uhr Daniel Hug:
Poisson polyhedra in high dimensions
Freitag, 17.01.2014
9.45 Uhr Daniel Hug:
Intersection and proximity of processes of flats
Freitag, 24.01.2014
9.45 Uhr Steffen Winter:
Skalierungsexponenten von Krümmungsmaßen
Abstract: Fractal curvatures of a subset F of R^d are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets F_e as e tends to 0 and have been studied in the last years in particular for self-similar and self-conformal sets. This previous work was focussed on establishing the existence of (averaged) fractal curvatures and related fractal curvature measures in the generic case when the k-th curvature measure C_k(F_e,.) scales like e^(k-D), where D is the Minkowski dimension of F. In the present paper we study the nongeneric situation when the scaling exponents do not coincide with the dimension. We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R^2. We expect local flatness to be characteristic also in higher dimensions.
The results enlighten the geometric meaning of the scaling exponents.
Freitag, 07.02.2014
9.45 Uhr Anne Marie Svane: