Topics in High-Dimensional Probability

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):
Francesco Pedrotti

If you want to enroll to this course, please click: REGISTER