AG Stochastische Geometrie (Sommersemester 2013)
- Dozent*in: Prof. Dr. Daniel Hug, Prof. Dr. Günter Last
- Veranstaltungen: Seminar (0175700)
- Semesterwochenstunden: 2
Forschungsseminar der Arbeitsgruppe Räumliche Stochastik und Stochastische Geometrie
| Termine | ||
|---|---|---|
| Seminar: | Freitag 9:45-11:15 | 1C-01 |
| Lehrende | ||
|---|---|---|
| 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 | ||
Vorträge
Wenn nicht explizit anders angegeben, finden die Vorträge im Raum 1C-01 (Allianzgebäude, Kaiserstr. 89) statt.
Freitag, 19.04.2013
10.00 Uhr Evgeny Spodarev (Uni Ulm):
ASYMPTOTIC GEOMETRY OF EXCURSION SETS OF NON–STATIONARY GAUSSIAN RANDOM FIELDS Abstract
Freitag, 26.04.2013
9.45 Uhr Matthias Schulte: DIE MALLIAVIN-STEIN-METHODE FÜR POISSON-FUNKTIONALE
Freitag, 03.05.2013
9.45 Uhr Matthias Schulte:
SOME CENTRAL AND NON-CENTRAL LIMIT THEOREMS IN STOCHASTIC GEOMETRY
Freitag, 10.05.2013
9.45 Uhr Anne-Marie Svane (Aarhus/Karlsruhe):
LOCAL ALGORITHMS FOR THE ESTIMATION OF INTRINSIC VOLUMES
- Abstract: Local algorithms are being used as a fast tool for estimating intrinsic volumes from digital images. In this talk I will explain these algorithms and give an overview over some of the known convergence results. Moreover, I will discuss possible generalizations for tensor valuations.
Freitag, 17.05.2013
9.45 Uhr Christoph Thäle (Uni Bochum): COMBINATORICS OF RANDOM TESSELATIONS
Freitag, 24.05.2013
9.45 Uhr Andreas Bernig (Uni Frankfurt):
CENTROID BODIES AND THE CONVEXITY OF AREA FUNCTIONALS
- Abstract: We introduce a new volume definition on normed spaces which is related to centroid bodies and random simplices. We show that it has strong convexity properties. Based on this, we prove that 2-dimensional flat discs are minimal with respect to Busemann's definition of volume.
Dienstag, 18.6.2013, Raum Z1 (Zähringerhaus, Fritz-Erler-Str. 3)
15.45 Uhr Yogeshwaran Dhandapani (Technion, Haifa):
UNDERSTANDING THE TOPOLOGY OF THE BOOLEAN MODEL
- Abstract: In this talk, we shall look at the well-known Boolean model but from a topological perspective. In particular, i shall describe results about the growth of Betti numbers in the Boolean model for various point processes. The Betti numbers count the number of components, voids, cavities and so on and hence are useful quantitative descriptors of the topology. Alternatively, one can define the distance function of a point process and count its critical points, called as the Morse critical points. The proof techniques for analysis of both Betti numbers and Morse critical points are connected to study of subgraph and component counts of the underlying random geometric graph.
The talk shall not assume any knowledge of advanced topology or probability.
Montag, 1.7.2013, 15.45 Uhr, Sitzungszimmer (Raum 5C-01, Allianzgebäude)
Fabian Gieringer: KONZENTRATIONSUNGLEICHUNGEN GEOMETRISCHER FUNKTIONALE
- Abstract: Da die Verteilung eines geometrischen Funktionals in vielen Fällen weitgehend unbekannt ist, sind in diesem Zusammenhang Konzentrationsungleichungen von Interesse. Diese schätzen die Wahrscheinlichkeit ab, mit der ein Funktional einen bestimmten Abstand zu seinem Erwartungswert überschreitet und geben somit neue Hinweise auf die Verteilung des Funktionals. Dieser Vortrag stellt anhand konkreter Beispiele solche Ungleichungen vor, wie sie vor kurzem von Eichelsbacher, Raic und Schreiber (arXiv:1010.1665) entwickelt wurden.
Dienstag, 2.7.2013, 15.45 Uhr, Raum Z1 (Zähringerhaus, Fritz-Erler-Str. 3)
Karoly Bezdek (University of Calgary): ON A STRONG VERSION OF THE KEPLER CONJECTURE
- Abstract: We raise and investigate the following problem which one can regard as a
very close relative of the densest sphere packing problem. If the Euclidean
3-space is partitioned into convex cells each containing a unit ball, how
should the shapes of the cells be designed to minimize the average surface
area of the cells?
Freitag, 5.7.2013, 10 Uhr
Peter Eichelsbacher (Uni Bochum): CUMULANTS AND LARGE DEVIATIONS PROBABILITIES
- Abstract: The purpose of the talk is to establish moderate deviation principles and so-called large deviation probabilities for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations probabilities due to Rudzkis, Saulis, and Statulevičius. The applications are focused to stabilizing functionals in geometric probability.
Freitag, 12.7.2013, 10 Uhr
Matthias Reitzner (Uni Osnabrück): LARGE DEVIATION INEQUALITIES AND THE GILBERT GRAPH
- Abstract: Choose n iid points in some space. Talagrand defined a convex distance on this space of point sets and proved a large deviation inequality which is very useful in various problems.
In the first part of this talk the definition of convex distance is extended to binomial and Poisson point processes. A corresponding large deviation inequality is proved.
In the second part of the talk these results will be applied to the number of edges in the Gilbert graph.