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Self-­interacting random walks and statistical physics [MA5941]

Summer semester 2022

Prof. Pierre Tarrès, John von Neumann Gastprofessor

Homepage: at NYU Shanghai Pfeil

Lecturer: Prof. Pierre Tarrès

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(Recommended) requirements:

MA2409 probability theory, MA2404 Markov chains

Contents:

The aim of the course is to introduce to some generic techniques for the study of self-­interacting random walks, and to explain the links that appeared recently with statistical physics, in particular with the supersymmetric hyperbolic sigma model arising in random matrix theory, with a random Schrödinger operator and with the so‐called Dynkin isomorphism and Ray-­Knight local time approaches. More information can be found here.

Time and location

The lecture will take place in following rooms in the mathematics building in Garching-Forschungszentrum on the following days:
  1. Monday, April 25, 2022, 10:15-11:45 Slides Video Pfeil
  2. Thursday, April 28, 2022, 10:15-11:45 Slides Video Pfeil
  3. Friday, April 29, 2022, 14:15-15:45 in room MI 02.10.011 Slides Video Pfeil
  4. Monday, May 2, 2022, 10:15-11:45 in room MI 02.10.011 Slides Video Pfeil
  5. Monday, May 9, 2022, 10:15-11:45 in room MI 02.10.011 Slides Video Pfeil
  6. Friday, May 13, 2022, 14:15-15:45 in room MI 02.04.011 Slides Video Pfeil
  7. Monday, May 16, 2022, 10:15-11:45 in room MI 02.10.011 Slides Video Pfeil
  8. Friday, May 20, 2022, 14:15-15:45 in room MI 02.04.011 Slides Video Pfeil
  9. Monday, May 23, 2022, 16:30 in room 2.01.10, Parkring 11, Garching-Hochbrück Please note the different time and the different location! Zoom Link for this lecture Pfeil, Meeting ID: 629 1710 7124, Passcode: Pierre
  10. Friday, May 27, 2022, 14:15-15:45 in room MI 02.10.011
  11. Monday, May 30, 2022, 10:15-11:45 in room MI 02.10.011
  12. Wednesday, June 1, 2022, 10:15-11:45 in room MI 02.10.011
The lecture starts on Monday, April 25. There will be a live streaming via zoom. The lectures will be recorded.

Exam

The exam will be in oral form (30 minutes). Students demonstrate that they have gained deeper knowledge of definitions and main mathematical tools and results on self-interacting random walks, particularly linearly edge-reinforced random walk, vertex-reinforced jump process, and their link to statistical physics.

The exam takes place on July 12, 2022. Please register for the exam in TUM online before the end of June.