Probability and Stochastic Analysis - University of Bonn

Summer 2014: Selected Topics in Probability Theory - Gibbs measures and phase transitions (V5F2)

Date & Time

Wednesdays, 14:00-16:00 in Room 0.011, Endenicher Allee 60.

Course description

This course will contain several topics of rigorous statistical mechanics. We will give an introduction to the mathematical study of phase transitions in lattice models, with a special emphasis on the concept of Gibbs measure. We plan to discuss the following examples:

  • Ising model (magnetization phase transition)

  • Van der Waals-Maxwell theory of Condensation (liquid-vapor phase transition)

  • The discrete Gaussian Free Field (interface model, study of thermodynamic limit of Gaussian fields)



The recommended prerequisites include basic probability theory (law of large numbers, central limit theorem, a little combinatorics, Gaussian vectors, random walks) and basic measure theory. We plan to introduce all the other tools in a self-contained way.