Selected Topics in Probability Theory: Mathematical Statistical Physics
|Start of the lecture:||October 10, 2023|
Room 0.011, Mathematics Centre
|Time:||Tuesday 16 - 18,|
Content: The focus of this course will be the theory of phase transitions in so-called lattice spin systems. This is basically the question of existence and uniqueness/nonuniqueness of infinite volume Gibbs measures. We will start with the basic definition and construction of Gibbs measures for interacting spin systems, the simplest instance being the celebrated Ising model. We will learn the basic tools to address these questions, as there are the Dobrushin uniquess creterium, the Peierls argument, cluster expansions, and correlation inequalities. After that, the topics we can choose depend on the interests of the participants.
The lectures are mainly based on my book on Statistical Mechanics of Disordered Systems.
- Anton Bovier. Statistical Mechanics of Disordered Systems. A mathematical perspective. Cambridge University Press, Cambridge, 2006
Hans-Otto Georgii,. Gibbs measures and phase transitions. De Gruyter 1988
Sascha Friedli and Yvan Velenik. Statistical mechanics of lattice systems. A concrete mathematical introduction. Cambridge University Press, Cambridge, 2018.
Barry Simon. Statistical mechanics of lattice gases. Princeton University Press, 1993
Exams : The examination will be oral.