# Interacting Particle Systems (5 points)

Class times!!!!!
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
COURSE GOAL:
Give an introduction to the subject of Interacting particle systems which
is an extremely exciting and active area in probability theory.

TIME:
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.

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

WHAT ARE INTERACTING PARTICLE SYSTEMS?
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.

PRELIMINARY TOPICS TO BE COVERED:
• The linear "voter" model on Z^d.
• The "contact" process on Z^d.
• The "contact" process on homogeneous trees.
• The exclusion process.

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

Course literature:
(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).

#### 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.

Kursexaminator:
Jeff Steif (steif@math.chalmers.se)