- Lecturer
- Vincent Tassion
- Coordinator
- Laurin Köhler-Schindler

Percolation theory has many applications and is one of the most famous model to describe phase transition phenomena in physics. One reason for this success is the variety of mathematical tools, which allows for a precise and rigorous description of the models. The objective of this course is to gain familiarity with the methods of the percolation theory and to learn some of its important results.

Outline of the course:

- Definition of percolation
- Standard tools: FKG inequality, BK inequality, Mixing property, and Russo's formula.
- Sharpness of the phase transition
- Correlation length and interpretations
- Uniqueness of the infinite cluster
- Critical percolation in dimension 2
- Supercritical percolation in dimension d>2
- Grimmett-Marstrand Theorem and consequences

From November 2, the lectures take place via zoom each Tuesday at 10.15am. The link was sent on November 2 by email. If you are a registered student and you need the link to be sent again, you can contact the coordinator of the class.

Three exercise classes are scheduled for October 13, November 10, and December 15 (replacing the regular lecture).

The forum can be accessed here. You are welcome to ask questions related to the content of the lectures as well as the exercises.

Regularly updated lecture notes can be found here.

In addition, the slides from the first lecture can be found below.

Every week, a new exercise sheet is uploaded here (starting in the second week). Exercises that are marked with a star (*) can be handed in for correction (usually one per sheet). You can send them by email to laurin.koehler-schindler@math.ethz.ch or hand in before the lecture.

- Exercise sheet 1
- Exercise sheet 2
- Exercise sheet 3
- Exercise sheet 4
- Exercise sheet 5
- Exercise sheet 6
- Exercise sheet 7
- Exercise sheet 8
- Exercise sheet 9

- "Percolation" by Geoffrey Grimmett (Springer, 1999)
- "Percolation" by Béla Bollobás und Oliver Riordan (Cambridge University Press, 2006)
- Introduction to percolation theory by Hugo Duminil-Copin (Lecture notes, 2018)