Oberseminar Wahrscheinlichkeitstheorie und andere Vorträge im Wintersemester 2021/22

Organisers: Nina Gantert (TUM), Noam Berger (TUM), Markus Heydenreich (LMU), Franz Merkl (LMU), Silke Rolles (TUM), Konstantinos Panagiotou (LMU), Sabine Jansen (LMU),

Talks:

Monday, 11th October 2021, 16:30, LMU, room B252, Theresienstr. 39, Munich
Hybrid meeting: Synchronous broadcast via zoom via the link (Click here for Zoom Meeting)
Detlev Kreß (LMU; MSc presentation)
Title: A percolation model without positiv correlattion
Abstract: We introduce a bond-percolation model that is a modification of the corrupted compass model introduced by Christian Hirsch, Mark Holmes and Victor Kleptsyn (2021).On a given graph we start in each vertex independent with probability p a random walk of length L. We make an edge occupied if it was used by a random walk. This model does not exhibit positive correlation.If L is choosen such that there is percolation for p=1, we have a sharp phase transition for p. We discuss the question of percolation on the hypercubic lattice and show that on the square lattice percolation occurs for L=2.

Monday, 25th October 2021, 16:30, LMU, room B252, Theresienstr. 39, Munich
Hybrid meeting: Synchronous broadcast via zoom via the link (Click here for Zoom Meeting)
Wolfgang Löhr (Universität Duisburg-Essen)
Title: A new state space of algebraic measure trees for stochastic processes
Abstract: In the talk, I present a new topological space of ``continuum'' trees,
which extends the set of finite graph-theoretic trees to uncountable
structures, which can be seen as limits of finite trees. Unlike previous
approaches, we do not use the graph-metric but formalize the tree-structure
by a tertiary operation on the tree, namely the branch-point map. The
resulting space of algebraic measure trees has coarser equivalence classes
than the more classical space of metric measure trees, but the topology
preserves more of the tree-structure in limits, so that it is incomparable
to, and not coarser than, the standard topologies on metric measure trees.
With the example of the Aldous chain on cladograms, I also illustrate that
our new space can be very useful as state-space for stochastic processes in
order to obtain path-space diffusion limits of tree-valued Markov chains.

Monday, 8th November 2021, 16:30, LMU, room B252, Theresienstr. 39, Munich
Hybrid meeting: Synchronous broadcast via zoom via the link (Click here for Zoom Meeting)
Sebastian Müller (Aix-Marseille Université)
Title: TBA

Monday, 15th November 2021, 16:30, LMU, room B252, Theresienstr. 39, Munich
Online meeting via zoom: (Click here for Zoom Meeting)
Johannes Krebs (KU Eichstätt)
Title: Statistical topological data analysis
Abstract: We study selected statistical and probabilistic topics in persistent homology, which is the major branch of topological data analysis (TDA). TDA itself refers to a collection of statistical methods that find topological structure in data. Persistent homology is a multiscale approach to quantifying topological features in data, in particular, point cloud data.After a short and heuristic introduction to the main ideas of persistent homology, we will study multivariate and functional central limit theorems (CLT) and related stabilizing properties for persistent Betti numbers in the critical regime. Based on the multivariate CLT, we consider a smooth bootstrap procedure to construct confidence intervals. More- over, using a functional central limit theorem, we derive goodness-of-fit test in order to compare network structures for different types of underlying point processes.

Monday, 20th December 2021, 16:30, LMU, room B252, Theresienstr. 39, Munich
Hybrid meeting: Synchronous broadcast via zoom via the link (Click here for Zoom Meeting)
Tom Kaufmann (Universität Bochum)
Title: TBA

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