Syllabus
Interacting particle systems, contact process, voter model, Ising model, exclusion process, mean-field model, duality, invariant measure, phase transition.
Annotation
Interacting particle systems are collections of locally interacting
Markov processes, situated on a lattice. While the process at a single lattice point is usually a very simple, finite state Markov process, the interaction between neighbours causes the system as a whole to show interesting behaviour, such as phase transitions.
The study of interacting particle systems started in the early 1970-ies motivated by problems from theoretical physics. Since that time, the field underwent a growth, with links to and applications in many other fields of science.
For PhD students.