Probability Seminar Essen
The seminar will start on November 3rd in form of video conference.
|Nov 10||Matthias Erbar (University of Bielefeld) - organized jointly with the SPP 2265-Research Seminar Ruhr.|
|Nov 17||Sandra Palau (UNAM, Mexico)|
|Nov 24||Zakhar Kabluchko (University of Münster) - organized jointly with the SPP 2265-Research Seminar Ruhr.|
|Dec 1||Lukas Gonon (LMU, Munich)|
|Dec 8||Lisa Hartung (University of Mainz) - organized jointly with the SPP 2265-Research Seminar Ruhr.|
|Dec 15||Jiequn Han (Princeton University)|
|Dec 22||Arno Siri Jégousse (UNAM, Mexico)|
|Jan 12||Eva Kopfer (University of Bonn) - organized jointly with the SPP 2265-Research Seminar Ruhr.|
|Jan19||Gilles Bonnet (University of Bochum) - organized jointly with the SPP 2265-Research Seminar Ruhr.|
|Jan 26||Christian Beck (ETH Zurich)|
|Feb 2||Alexander Drewitz (University of Cologne) - organized jointly with the SPP 2265-Research Seminar Ruhr.|
|Feb 9||Felix Lindner (University of Kassel)|
Matthias Erbar (University of Bielefeld)
Abstract: In this talk I would like give an overview of the topics and aims of the project "Optimal transport for stationary point processes" within the SPP "Random geometric systems". I will give a brief introduction of the classical theory of optimal transport for finite measures and will outline how we envision to develop a counterpart to this theory in the setting of stationary point processes. I will also present first results in this direction from joint work with M. Huesmann and T. Lebl\'e which apply ideas from optimal transport in the study of log gases. The one-dimensional log gas in finite volume is a system of particles interacting via a repulsive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sine_\beta process constructed by Valko and Virag. We show that this process can be characterized as the unique minimizer of a renormalized free energy by leveraging strict convexity properties of this functional along interpolations built via optimal transport.
|Nov 17||Sandra Palau (UNAM, Mexico)
Branching processes in varying environment
Abstract: In this talk we are going to study branching processes and its extension when the offspring distribution is varying over time. We are going to analyze its extinction probability. By using a two-spine decomposition technique we are going to give the law of the process conditioned on non extinction.
Zakhar Kabluchko (University of Münster)
We shall define and study several families of random tessellations of the Euclidean space, the sphere and the hyperbolic space that generalize the classical Poisson-Voronoi and Poisson-Delaunay tessellations. The talk is based on a joint work with Anna Gusakova and Christoph Thäle.
Lukas Gonon (LMU, Munich)
We study the expression rates of deep neural networks for option prices written on high-dimensional baskets of risky assets, whose log-returns are modelled by a multivariate Lévy process with general correlation structure of jumps. We establish sufficient conditions on the characteristic triplet of the Lévy process that ensure that the size of the DNN required to achieve a given approximation accuracy grows only polynomially with respect to the dimension of the Lévy process and the reciprocal of the approximation accuracy, thereby overcoming the curse of dimensionality and justifying the use of DNNs in financial modelling of large baskets in markets with jumps.
Arno Siri Jégousse (UNAM, Mexico)
In this talk, I will study the concept of site frequency spectrum (SFS), which happens to be one of the most relevant statistics in population genetics. It is of particular use for genealogical model selection and estimation in evolution models. The SFS is closely related to the shape of the genealogical tree of the observed sample of a population.