Department Mathematik



                                  Reading Seminar
                        Interacting Particle Systems

                                            Summer semester 2021

There are many beautiful problems of a physical type that can be modelled as a Markov process on the space {0,1}^V (where V is the set of vertices of a graph). Such processes are interacting particle systems, prominent examples include the contact process, the voter model, the exclusion process as well as the stochastic Ising model. Thomas Liggett has brought this theory to maturity, and in this reading course we want to derive the mathematical theory of interacting particle systems from the rather general theory of Feller processes.

Target group: This reading course is intended as a continuation of the master course Stochastic processes in the last winter semester and is directed to students who passed this course and want to know more about this fascinating topic.

Lecturer: Markus Heydenreich

Registration: Please send an email to the lecturer.

Time:  Occasional meetings. Time by agreement.

Our main text is Chapter 4 of the textbook Continuous Time Markov Processes by Thomas Liggett (AMS 2010), as well as Chapters 6 and 10 in Probability on Graphs by Geoffrey Grimmett (second edition; Cambridge University Press 2018). For background and in-depth reading there are the classical volumes Interacting particle systems and Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, both by Thomas Liggett (Springer, 1985 and 1999). We shall also target more specialised topics depending on the interest of the participants (literature for this provided later).