## 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)

#### Literature

S.Friedli and Y. Velenik,

*Equilibrium Statistical Mechanics of Classical Lattice Systems: a Conrete Introduction.*Project of Book to be downloaded at: www.unige.ch/math/folks/velenik/smbook/index.html

#### Prerequisites

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.