Spatial Probability & Statistical Mechanics (MA6000D)

Semester I 2007-8

This course is for the EPSRC-funded Taught Course Centre, with lectures being broadcast interactively to collaborating universities (Bath, Bristol, Imperial, Oxford, Warwick).

Provisional list of topics

1. Review of probability (very brief)
2. Ergodic Theory.
3. Percolation
4. The Ising model and random-cluster models.
5. First passage percolation.
6. Interacting particle systems.

Books on general probability background (Sec.1-2)

R. Durrett: Probability: Theory and Examples (1st ed. 1991).
G. R. Grimmett and D. R. Stirzaker: Probability and Random Processes.
D. Williams: Probability with Martingales.

Books on Sections 3-6

R. Durrett: Lectures on Particle Systems and Percolation (possibly not in print).
G. Grimmett: Percolation.
G. Grimmett: The Random-Cluster Model.
T. Liggett: Interacting Particle Systems.