Interacting Particle Systems

Lecture:
Dates:

Tuesdays, 9:00 to 12:00 in room B 046 at Theresienstr. 39 (LMU München) in Munich

Start: 16th October 2012

Instructor:Prof. Dr. Nina Gantert
Prerequisites:Probability Theory
Content:

"Interacting particle systems" is a large and growing field of probability theory that gives a rigorous analysis of certain models that arise in statistical physics, biology, economy and other fields. In this lecture, we provide an introduction to some of these models, give some basic results about them and explain the most important tools used in their study. We will treat the contact process which describes the spread of an infection, the voter model and the Ising model. These are Markov processes on a (huge) space of spin configurations. In contrast to finite Markov chains, there can be several equilibria for the same dynamics. For instance, the Ising model exhibits a phase transition for large values of the temperature. We will treat some Markov process theory (generators, semigroups) and some important techniques as coupling and duality.

Literature:

Liggett, Tom: Continuous Time Markov Processes: an introduction
Liggett, Tom: Interacting Particle Systems

If you have any questions concerning the exercise classes, please contact Prof. Dr. Nina Gantert.