Webrelaunch 2020

AG Stochastische Geometrie (Wintersemester 2021/22)

Studierende und Gäste sind jederzeit herzlich willkommen. Wenn nicht explizit anders unten angegeben, finden alle Vorträge in Präsenz im Raum 2.058 statt. Für die Aufnahme in den E-Mail-Verteiler für die Einladungen kontaktieren Sie bitte Steffen Winter (steffen.winter@kit.edu).

Seminar: Freitag 10:00-11:30 20.30 SR 2.58
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

Freitag, 4.2.2022, 10 Uhr (Raum 2.058 mit Zoom-Option)

Daniel Hug

Curvature measures, Steiner-type formula and Alexandrov theorem in Minkowski–Finsler spaces

Freitag, 28.1.2022, 10 Uhr (Raum 2.058 mit Zoom-Option)

Julia Hörrmann (ETH Zürich)

Reconstruction of convex bodies from moments

Abstract: We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are uniquely determined by a finite number of moments form a dense set. Further, we derive a stability result for convex bodies based on geometric moments. It turns out that the stability result is improved considerably by using another set of moments, namely Legendre moments. We present a reconstruction algorithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stability result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under certain assumptions on the variance of the noise variables.

Freitag, 21.1.2022, 10 Uhr (Raum 2.058 mit Zoom-Option)

Günter Last

Poisson hulls and nonparametric boundary estimation

Abstract: We consider a hull operator acting on a (general) Poisson point process. One key example is the convex hull of the support of a Poisson process on a convex body. Another example is a Poisson process of certain Lipschitz functions (on Euclidean space) lying above a given curve. The hull is then the pointwise minimum of the functions in the Poisson process. Assuming that the intensity measure of the process is known on the set generated by the hull operator, we discuss estimation of a linear statistics built on the Poisson process. In the above special cases, our general scheme yields the estimator of the volume of the convex body or of some integral characteristics of the boundary function, respectively. An interesting feature is that these estimators are stochastic Kabanov-Skorohod integrals. This fact is a consequence of a stopping property of the hull operator. Under suitable assumptions we use the Stein-Malliavin method to derive the rate of normal convergence for the estimation error.

The talk is based on joint work with Ilya Molchanov (Bern).

Freitag, 10.12.2021, 10 Uhr (Raum 2.058)

Alexander Zass (WIAS Berlin)

Gibbs point processes on path space: existence, cluster expansion and uniqueness

Abstract: In this talk we present a class of infinite-dimensional diffusions under Gibbsian interactions, viewed in the context of marked point configurations: the starting points belong to \mathbb{R}^d, the marks are the paths of Langevin diffusions, and the interaction between two diffusions is given by the integration of a pair potential along their paths. Motivated by this example, we first prove the existence of an infinite-volume Gibbs point process by adapting a general entropy method result to the setting of pair potentials. We then provide an explicit activity domain in which uniqueness holds by using cluster expansion tools.

Dienstag, 7.12.2021, 16 Uhr (Raum 2.059, zum Termin der AG Stochastik)

Matthias Neumann (Universität Ulm)

Random set models for three-phase electrode materials with an emphasis on transport relevant characteristics

Abstract: pdf

Freitag, 29.10.2021, 10 Uhr (Raum 2.058)

Günter Last

Poisson approximation for subcritical Gibbs processes

Abstract: We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach taken in Hofer-Temmel and Houdebert (2019), we will use this to couple two finite Gibbs processes with different boundary conditions. Combining this coupling with a classical result from Barbour and Brown (1992), we establish Poisson approximation of point processes derived
from certain subcritical Gibbs processes via dependent thinning.
The talk is based on joint work with Moritz Otto.

Montag, 11.10.2021, 11:30 - 17:10 Uhr (in Bern, mit Zoom-Option)

First HiBeKi Meeting

Gemeinsamer Workshop der Arbeitsgruppen Computational Statistics am HITS in Heidelberg, Stochastik am IMSV in Bern und Stochastische Geometrie am KIT in Karlsruhe. Programm