Webrelaunch 2020

AG Stochastische Geometrie (Wintersemester 2020/21)

Studierende und Gäste sind jederzeit herzlich willkommen. Wenn nicht explizit anders unten angegeben, finden alle Vorträge als Zoom-Meeting statt. Den Beitrittslink finden Sie in der jeweiligen Einladung zum Vortrag. 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 SR 2.058
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

Donnerstag, 29.10.2020, 14 Uhr (Zoom Meeting)

Viktor Bezborodov (Wroclaw University of Science and Technology)

Stochastic growth models

Abstract: We discuss stochastic particle growth models and their asymptotic growth rate. At the beginning we talk about classic stochastic growth models. We then proceed to more recent research such as a continuous-space birth process and a branching random walk with restriction. We conclude by discussing the spread rate of a continuous-time frog model.

Freitag, 13.11.2020, 10 Uhr (Zoom Meeting)

Mikhail Chebunin (Novosibirsk State University, Russia)

Limit theorems for two classes of stochastic models under information incompleteness conditions

Abstract: In this talk, we will deal with (A) statistical estimates and (B) stochastic algorithms (protocols) in the presence of incomplete information, which is frequently the case in probability and statistics. I will present results for two types of stochastic models. In model A, I will study the asymptotic properties of the number of different elements in a sample from distribution on the positive integers, which is taken from a one-parametric family of distributions. In model B, I will study stability and instability conditions for a multiple access information transmission system (``ALOHA-type"): time is slotted (integer-valued), messages arrive in an i.i.d. input; they cannot make a queue (no direct communication), and only one of them may be transmitted per unit of time. The only way to have successful transmissions is to allow a message to make a transmission attempt at random, with a probability that depends on certain system information.

Freitag, 4.12.2020, 10 Uhr (Zoom Meeting)

Günter Last (KIT)

A hyperflucuating and strongly rigid point process

Freitag, 29.01.2021, 10 Uhr (Zoom Meeting)

Günter Last (KIT)

The OSSS variance inequality for Poisson processes

Abstract: We present a continuum version of the OSSS variance inequality, proved by O'Donnell, Saks, Schramm and Servedio (2005) for randomized algorithms. To do so we consider a Poisson process \eta on a general Borel space with a diffuse intensity measure. We then introduce the concept of a continuous-time decision tree (CTDT), which is a family of stopping sets increasing in time. If such a CTDT approaches a stopping set $Z$ in a continuous manner, then the OSSS inequality holds for any binary functional of \eta which is determined by the restriction of \eta to $Z$. We apply this result to prove sharp phase transition for k-percolation of the Poisson Boolean model with bounded grains and for confetti percolation.
This is joint work with G. Peccati (Luxembourg) and D. Yogeshwaran (Bangalore).

Freitag, 19.02.2021, 10 Uhr (Zoom Meeting)

Daniel Hug (KIT)

Extremizers and stability of the Betke-Weil inequality

Abstract: Let K be a compact convex domain in the Euclidean plane. The mixed area A(K,-K) of K and -K can be bounded from above by 1/(6\sqrt{3})L(K)^2, where L(K) is the perimeter of K . This was proved by Ulrich Betke and Wolfgang Weil (1991). They also showed that if K is a polygon, then equality holds if and
only if K is a regular triangle. We prove that among all convex domains, equality holds only in this case, as conjectured by Betke and Weil. This is achieved by establishing a stronger stability result for the geometric inequality 6\sqrt{3}A(K,-K)\le L(K)^2.