Talks in 2012

Vortrag im Seminar Diskrete Mathematik und Optimierung

Title: Random Walks on critical Percolation-Trees
Speaker: Florian Sobieczky (University of Denver)
Date: 18.12. 2012, 14:15
Room: Seminarraum C208, Steyrergasse 30, 2. Stock

Bounds for the expected return probability of the delayed random walk on
finite clusters of an invariant percolation on transitive unimodular
graphs are derived. They are particularly suited for the case of critical
Bernoulli percolation and the associated heavy-tailed cluster size
distributions. The upper bound relies on the fact that cartesian products
of finite graphs with cycles of a certain minimal size are Hamiltonian.
For critical Bernoulli bond percolation on the homogeneous tree this bound
is sharp. The asymptotic type of the expected return probability for large
times t in this case is of order of the 3/4'th power of 1/t.

Joint Seminar

Title: Lumped Markov chains and entropy rate preservation
Speaker: Bernhard Geiger and Christoph Temmel (TU Graz)
Date: 10 Dez, 16:00
Room: IDEG134

A lumping of a Markov chain is a coordinate-wise projection of the chain. We characterize the entropy rate loss of a lumping of a stationary Markov chain on a finite state space in two ways. First, by the asymptotic ratio of the number of trajectories with positive weight between the original and the lumped chain. Second, by the reconstructability of original trajectories from their images under the lumping. Every non-trivial lumping of a Markov chain with positive transition matrix incurs an entropy rate loss. We give sufficient conditions on the non-positive transition matrix and the lumping to preserve the entropy rate. In the sparse setting we state sufficient conditions on the lumping to both preserve the entropy rate and result in a k-th order homogeneous Markov chain.

Kolloquium: Mathematische Methoden in den Natur- und Ingenieurwissenschaften

Title: Gauss, Jacobi, Seidel, Richardson, Krylov: The Invention of Iterative Methods
Speaker: Univ.-Prof. Dr. Martin J. GANDER (Universität Genf)
Date: Freitag, 7.12.2012, 16:00 Uhr
Room: TU Graz, Steyrergasse 30, 3. Stock, Seminarraum C307


Title: Optimal Transport, Model-Indepedence, and Trajectorial Inequalities.
Speaker: Mathias Beiglböck (Universität Wien)
Date: Freitag, 7.12.2012, 14:15 Uhr
Room: Seminarraum A206, Steyrergasse 30, 2.Stock, Geodäsie

We will explain a recently discovered connection between Optimal
Transport and the areas of model independence / martingale
inequalities in probability. This link has a number of fruitful
consequences. For instance, the duality theorem from optimal transport
leads to new super-replication results. Optimality criteria from the
theory of mass transport can be translated to the martingale setup and
allow to characterize minimizing/maximizing models in finance.
Moreover, the dual viewpoint provides new
insights to the classical inequalities of Doob and Burkholder-Davis-Gundy.