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Percolation Theory
Last Updated: 2026-06-03 00:14:18
Abstract
An introduction to the percolation theory.
Objective
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. The students will develop their background and intuition in probability, and the course is particularly recommended to students with additional interests in physics or graph theory.
Content
Definition of percolation. Standard tools: FKG, Spatial Markov Property, Mixing property, Russo's formula. Sharpness of the phase transition. Correlation length and interpretations. Uniqueness of the infinite cluster. Critical percolation in dimension Supercritical percolation in dimension d>2, Grimmett-Marstrand Theorem and consequences.
Resources
Literature
B. Bollobas, O. Riordan: Percolation, CUP 2006 G. Grimmett: Percolation 2ed, Springer 1999
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- DR , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Percolation Theory |
|
2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)
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Doctorate Mathematics (More Information at: )
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Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
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Graduate School (Official website of the Zurich Graduate School in Mathematics: )
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