Forschungsseminar der Arbeitsgruppe Räumliche Stochastik und Stochastische Geometrie

Vorträge

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

Freitag, 24.10.2014

9.45 Uhr Matthias Schulte:

Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem

Freitag 07.11.2014

9.45 Uhr Daniel Hug:

Isotrope Maße und Stabilität der umgekehrten isoperimetrischen Ungleichung

Freitag 14.11.2014

9.45 Uhr Christian Hirsch (Weierstraß-Institut)

From heavy-tailed Boolean models to scale-free Gilbert graphs

Abstract: Define the scale-free Gilbert graph based on a Boolean model with heavy-tailed radius distribution on the d-dimensional torus by connecting two centers by an edge if at least one of the balls contains the center of the other. We investigate two asymptotic properties of this graph as the size of the torus tends to infinity:
i) the tail index associated with the asymptotic distribution of the sum of all power-weighted incoming and outgoing edge lengths at a randomly chosen vertex.
ii) chemical distances between distant nodes.

Freitag 21.11.2014

9.45 Uhr Philipp Schönhöfer (Friedrich-Alexander-Universität Erlangen-Nürnberg)

Minkowski Funktionale von Fraktalen Geometrien

Freitag 28.11.2014

9.45 Uhr Daniel Hug:

Isotrope Maße und Stabilität der umgekehrten isoperimetrischen Ungleichung - Teil II

Freitag 05.12.2014

9.45 Uhr Claudia Redenbach (TU Kaiserslautern)

Estimation of fibre length distributions from CT image data

Abstract: Fibre composites are nowadays used in a wide range of application areas. Prominent examples are glass or carbon fibre reinforced polymers which are used for the production of cars or airplanes. It is well known that the macroscopic properties of a fibre composite are highly dependent on geometric characteristics of the fibre system such as the fibre volume fraction or the fibre direction distribution. These quantities can be estimated from tomographic image data.

A problem which is still widely unsolved is the estimation of the fibre length distribution. A straightforward approach would be to segment single fibres in the image to obtain an empirical estimate of the length distribution. In practice, this approach is hampered by limitations of the imaging devices. If the resolution is chosen high enough to resolve single fibres, most fibres will be cut off by the image boundary. This introduces a severe censoring of the length data. We suggest two different approaches for the estimation of the fibre length distribution which take these effects into account.

Freitag 12.12.2014

9.45 Uhr Ferenc Fodor (University of Szeged)

Generating random hulls by congruent balls

Freitag 09.01.2015

9.45 Uhr Antti Käenmäki (University of Jyväskylä)

Dynamics of the scenery flow, conical densities, and rectifiability

Abstract: We present applications of the recently developed ergodic theoretic machinery on scenery flows to classical geometric measure theoretic problems in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main results include a sharp version of the conical density theorem, which we reduce to a question on rectifiability.

Freitag 16.01.2015

9.45 Uhr Sebastian Ziesche

Die Ornstein-Zernike Gleichung im Booleschen Modell

Freitag 23.01.2015

9.45 Uhr Martina Zähle (Friedrich-Schiller-Universität Jena), Sitzungszimmer der Fakultät (Raum 5C-01)

Geometrie gestern und heute - ein Streifzug durch gekrümmte Räume

Abstract: Anhand eines speziellen euklidischen Invariantensystems – den stetigen bewegungsinvarianten Valuationen – machen wir einen Streifzug durch die Geometrie der letzten einhundertfünfzig Jahre. Konvexgeometrie, Differentialgeometrie, geometrische Maßtheorie und algebraische Geometrie erlauben mittlerweile verschiedene Zugänge zu diesen Funktionalen und ihren Maßversionen auf unterschiedlichen Mengenklassen. Die Basiselemente sind z.B. als Quermaßintegrale oder als Lipschitz-Killing-Krümmungen und (niederdimensionale) Volumina bekannt, und die Euler-Charakteristik ist eingeschlossen.
Mit Hilfe fraktaler Varianten kann man nun auch die Geometrie gewisser Klassen von (zufälligen) fraktalen Mengen genauer beschreiben. Hier sind die Erneuerungstheorie und dynamische Systeme ein wichtiges Hilfsmittel.

Freitag 30.01.2015

9.45 Uhr Andreas Reichenbacher

Über das Kendall'sche Problem

Freitag 06.02.2015

9.45 Uhr Kirstin Strokorb (Universität Mannheim)

Comonotonic max-stable processes

Abstract: It is well-kown that, under very mild conditions, max-stable processes can be represented as the maximum of the points of a Poisson process whose intensity measure satisfies some scaling properties. We shall single out a subfamily of max-stable laws that arises from a particular (but very natural) choice of the intensity of the intensity of the underlying Poisson process. We adopt the viewpoint that max-stable processes are stable random sup measures. It is shown how to associate a general stable random sup-measures with a special one, whose principal feature is the comonotonic additivity of its tail dependence functional.
(joint work in progress with Ilya Molchanov)

Freitag 13.02.2015

9.45 Uhr Sascha Bachmann (Universität Osnabrück)

Concentration Inequalities for Geometric Poisson Functionals

Abstract: In recent years, the investigation of functionals associated to a Poisson point process has been an active area of research. In this talk, methods to prove concentration inequalities for such functionals will be presented. The approach is based on logarithmic Sobolev inequalities and turns out to be quite useful in the context of random geometric graphs. In these graphs, the vertices are given by a Poisson point process and any two vertices are connected by an edge whenever their distance does not exceed some fixed positive real number. A natural quantity to consider is now for example the number of edges. The talk is based on joint work with Giovanni Peccati.