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AG Stochastische Geometrie (Wintersemester 2013/14)

Forschungsseminar der Arbeitsgruppe Räumliche Stochastik und Stochastische Geometrie

Seminar: Freitag 9:45-11:15 Seminarraum K2
Seminarleitung Prof. Dr. Daniel Hug
Sprechstunde: Nach Vereinbarung.
Zimmer 2.051 Kollegiengebäude Mathematik (20.30)
Email: daniel.hug@kit.edu
Seminarleitung Prof. Dr. Günter Last
Sprechstunde: nach Vereinbarung.
Zimmer 2.001, Sekretariat 2.056 Kollegiengebäude Mathematik (20.30)
Email: guenter.last@kit.edu


Wenn nicht explizit anders angegeben, finden die Vorträge im Raum K2 (Kronenstr. 32, Eingang ca. 10m links neben der Kaffeebar Schiller) statt.

Freitag, 25.10.2013

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 \mathfrak{m} and f(\cdot) be a stationary random tessellation and a functional defined on the set of convex bodies. Given a bounded subset W\subset \mathbf{R}^d, we investigate the order statistics of f(C) over all cells C\in\mathfrak{m} with nucleus in \mathbf{W}_{\rho}=\rho^{1/d}W when \rho\rightarrow\infty. Under suitable conditions, we show that the knowledge of the distribution tail of f(\mathscr{C}), where \mathscr{C} 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, 22.11.2013

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:

Local algorithms based on grey-scale images