2009 Probability Seminar - 01

For Markov random fields temporal mixing, the time it takes for the Glauber dynamics to approach it's stationary distribution, is closely related to the spatial mixing properties of the measure such as uniqueness and the reconstruction problem. Such questions are of importance in probability, statistical physics and theoretical computer science. I will discuss some recent progress in understanding the mixing time of the Glauber dynamics for the Ising model and for random colourings of graphs.