The course deals with the long-term behaviour of stochastic processes and related geometric and functional inequalities. Possible topics include logarithmic Sobolev inequalities, semigroup methods, optimal transport, Schrödinger bridges, stochastic localisation, and the Polchinski renormalisation flow.
References:
Roland Bauerschmidt, Thierry Bodineau, Benoit Dagallier
Stochastic dynamics and the Polchinski equation: an introduction ( https://arxiv.org/abs/2307.07619 )
Ronen Eldan
Analysis of high-dimensional distributions using pathwise methods ( https://www.wisdom.weizmann.ac.il/~ronene/files/Pathwise.pdf )
Target group: Graduate students in mathematics and related fields.
Prerequisites: Knowledge of calculus and elementary probability is required. Knowledge of measure theory is helpful.
Evaluation: Pass/fail based on homework exercises
Teaching format: Classroom lectures and homework exercises
ECTS: 3 Year: 2023
Track segment(s):
Elective
Teacher(s):
Jan Maas
Teaching assistant(s):
If you want to enroll to this course, please click: REGISTER
- Teacher: Jan Maas