Mondays 10:15-12:00 and Thursdays 13:15-15:00. Both times in room MD4.

Here are some background notes on ergodic theory (March 4 update)

Assignment 1

Assignment 2

Assignment 3

Give an introduction to the subject of Interacting particle systems which

is an extremely exciting and active area in probability theory.

This course will run in the spring (2004) and will start somewhere at the beginning of February.

It will meet somewhere between 2 and 4 hours a week.

This course is intended for graduate students in mathematics and mathematical statistics.

Faculty are also of course very welcome.

Interacting particle systems are systems of infinitely many particles (or agents) which evolve according to simple specified

"local stochastic" dynamics. These models have extremely rich and interesting "global behavior" and the goal is to understand

this "global behavior" based on the simple stochastic dynamics. For example, so-called "phase transitions" arise for these models.

For systems on the Euclidean lattice, one often has one "critical value" (at which the behavior of the system drastically changes

as a given parameter is varied) while on trees, one has the new phenomenon of two "critical values", a so-called double phase transition.

Some probability theory (ask me if you are unsure).

(1) Interacting particle systems-An introduction by Tom Liggett

(2) Some notes that I have written.

Both of these can be picked up from me at any time.

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

There will be some homeworks, a final oral exam and perhaps (depending on the

number of students) presentations of papers.

Jeff Steif (steif@math.chalmers.se)

Last modified: Sunday January 4 10:15:34 MET DST 2004