TU Dortmund
Fakultät für Mathematik

Percolation and Spin Systems (Sommersemester 2021)

General information

This lecture of the Graduiertenkolleg 2131 'High-dimensional Phenomena in Probability - Fluctuations and Discontinuity' takes place in cooperation between the Technische Universität Dortmund, the Ruhr Universität Bochum, and the Universität Duisburg-Essen and is held by Prof. Dr. Ivan Veselic (Dortmund) and Prof. Dr. Christof Külske (Bochum).

The lecture will be held in english and is aimed at PhD students and Masters students with advanced knowledge in analysis and some knowledge in stochastics. There is a Moodle site at the Ruhr Universität Bochum.

Contents and access

The course deals with complex systems as encountered in many areas of statistical mechanics. We focus on two of them: Percolation Theory and Spin Systems. They study large or infinite collections of random variables indexed by a geometric space, typically an Euclidean lattice or subsets thereof. Due to the interactions of the RV critical phenomena like phase transitions arise.

Percolation is certainly the simplest model in this class but many methods and paradigms encountered in this simple setting play a prominent role in Spin Systems as well. For this reason it is very attractive to study these two fields in parallel.

The part of the lecture by Ivan Veselic devoted to Percolation will follow quite closely the lecture notes by Vincent Tassion, see


In particular, if one misses a lecture it is possible to cover the ideas by reading the corresponding section in the notes by Tassion, even though some Lemmata and Examples may be different in our course. For background reading I recommend the book

Grimmett, Geoffrey: Percolation, Springer, Berlin, 1989.

which contains a detailed exposition and detailed proofs. However, certain results and proofs have been improved since 1989. For this reason we follow the more modern lecture notes of Tassion.

The course starts with a lecture on 12th April at 13:15 on Percolation theory as a zoom meeting.

The Link to the zoom meeting is (ID: 970 2961 4001 PW: 504716): https://ruhr-uni-bochum.zoom.us/j/97029614001?pwd=Rm43QjJsZkNSQ3FkQ2FWQjhMRi84Zz09

Further Literature (on Percolation)

Bollobás, Béla; Riordan, Oliver. Percolation. Cambridge University Press, New York, 2006. x+323 pp. ISBN: 978-0-521-87232-4; 0-521-87232-4, DOI 10.1017/CBO9781139167383

Chayes, Jennifer, Chayes, Lincoln: Percolation and random media. In: Phénomènes critiques, systèmes aléatoires, théories de jauge, North-Holland, Amsterdam, 1986.

Grimmett, Geoffrey: Percolation, Springer, Berlin, 1989.

Grimmett, Geoffrey R.; Kesten, Harry. Percolation theory at Saint-Flour. Probability at Saint-Flour. Springer, Heidelberg, 2012. xxviii+303 pp. ISBN: 978-3-642-32508-3

Hunt, A.; Ewing, R. Percolation theory for flow in porous media. Lecture Notes in Physics, 771. Springer-Verlag, Berlin, 2009. xviii+319 pp. ISBN: 978-3-540-89789-7

Kesten, Harry. Percolation theory for mathematicians. Progress in Probability and Statistics, 2. Birkhäuser, Boston, Mass., 1982. iv+423 pp. ISBN: 3-7643-3107-0

Meester, Ronald; Roy, Rahul. Continuum percolation. Cambridge Tracts in Mathematics, 119. Cambridge University Press, Cambridge, 1996. x+238 pp. ISBN: 0-521-47504-X, DOI 10.1017/CBO9780511895357

Stauffer, Dietrich. Introduction to percolation theory. Taylor & Francis, Ltd., London, 1985. viii+124 pp. ISBN: 0-85066-315-6

Werner, Wendelin. Percolation et modèle d'Ising. Cours Spécialisés , 16. Société Mathématique de France, Paris, 2009. vi+161 pp. ISBN: 978-2-85629-276-1



TU Dortmund
Fakultät für Mathematik
Lehrstuhl IX
Vogelpothsweg 87
44227 Dortmund

Sie finden uns auf dem sechsten Stock des Mathetowers.


Janine Textor (Raum M 620)

Tel.: (0231) 755-3063
Fax: (0231) 755-5219
Mail: janine.textor@tu-dortmund.de
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