Thesis topics
In winter term 2021/22, I am offering to supervise master theses on the following topics.
Email me if you are interested in one of these.
Berry-Esseen inequalities for martingales
Berry-Esseen inequalities are quantitative versions of the central limit theorem.
I am interested in martingale versions of these inequalities, which were introduced by Hall and Heyde.
The following questions can be addressed in a thesis on this topic.
- Dependence of tail estimates on moment conditions.
- Dependence of convergence rate on moment conditions.
- Functional version (convergence to Brownian motion).
Prerequisites: real and harmonic analysis (V4B5), stochastic analysis (V4F1)
Operator scaling and Brascamp-Lieb constants
Operator scaling is an algorithm for deciding invertibility of certain operators on the space of positive matrices.
For me, it is interesting because it can be applied to the computation of Brascamp-Lieb constants.
The following questions can be addressed in a thesis on this topic.
- Computing the exponent in scale-dependent Brascamp-Lieb inequalities.
- Computing the constant in scale-dependent Brascamp-Lieb inequalities.
- Local Hölder continuity of capacity (in the cited paper, it is proved at rational points; looking at neighborhoods of rational points would be interesting).
Prerequisites: real and harmonic analysis (V4B5), some numerics, summer school.