Interacting Particle Systems (7 1/2 points)
Spring 2011, 4th reading period
(approx. March 21st-May 20)

Class times and place
We will meet Tuesdays and Thursdays 13:15-15:00 in MVL15.
First class is March 22nd.
No classes April 5 and 7.


Assignment 1
Assignment 2
Assignment 3
Give an introduction to the subject of Interacting particle systems,
an exciting and active area in probability theory.

This course is intended for graduate students in mathematics and mathematical statistics.
Faculty are also of course very welcome.

Course Description
This course will give an introduction to the area of interacting
particle systems (IPS) by studying a few specific models which have
been of interest for quite some time. IPS are Markov processes which
govern systems describing the evolution of infinitely many agents
(or particles) which can be in a finite number of different states.
The state space describing the system is uncountable which allows
for new phenomena which cannot arise in countable state situations.
The Markov evolution is specified by elementary simple "local" rules
and yet interesting "global" phenomena such as phase transitions
occur. Two of the models we will study are the contact process and
the voter model.

  • The linear "voter" model on Z^d.
  • The "contact" process on Z^d.
  • The exclusion process.

    Reasonable experience in probability theory (feel free to come and
    discuss your background with me).

    Course literature:
    (1) Interacting particle systems-An introduction by Tom Liggett
    (2) Some notes that I have written.
    Both of these will be available soon to be picked up from me in my office.

    In case, you need a little background on continuous time Markov chains, here is a 14 page summary (in Swedish however).

    Introduction to Markov chains

    Examination Form:
    There will be some homeworks, a final oral exam and perhaps (depending on the
    number of students) presentations of papers.

    Jeff Steif (
    Last modified: Tuesday March 1 10:15:34 MET DST 2011