High-dimensional probabilistic problems arise in many areas of science. The basic question is often to find good upper and lower bounds for the fluctuations of high-dimensional random quantities. In this course we discuss some of the central mathematical ideas to attack such problems.
Possible topics include Markov semigroups, geometric and functional inequalities, Stein’s method, stochastic calculus, and optimal transport.
References
R. van Handel. Probability in High Dimension
S. Chatterjee. Superconcentration and Related Topics
D. Bakry, I. Gentil, M. Ledoux. Analysis and Geometry of Markov Diffusion Operators
Target group: PhD students from all years, postdocs, anyone else who is interested
Prerequisites: Knowledge of calculus and elementary probability is required. Basic knowledge of measure theory is helpful, but not required
Evaluation: pass/fail based on homework
Teaching format: classroom lectures, homework
ECTS: 3 Year: 2021
Track segment(s):
MAT-PROB Mathematics - Probability
Teacher(s):
Jan Maas
Teaching assistant(s):
If you want to enroll to this course, please click: REGISTER
- Teacher: Jan Maas