February 3, 2012Location: Janskerkhof 15a (Utrecht), room 001
I will discuss some models of stochastic growth processes where structures evolve according to very simple rules, but where it is nevertheless difficult to predict or understand the shape and typical size of these structures.
After an introduction, I will focus on recent and ongoing work (and state some challenging open problems) on one of these models, called ‘frozen percolation’. This model was introduced about twelve years ago by D. Aldous who was partly motivated by phenomena like sol-gel transitions.
Probabilistic Cellular Automata (PCA) are stochastic systems evolving according to a parallel rule on a discrete state space. At each time all the variables are updated simultaneously. For particular choices of this rule the chain has a stationary measure similar to the equilibrium measure of Statistical Mechanics lattice systems. In this case it is possible to study the existence of metastable states for the chain. The talk will focus on results for some particularly interesting PCA models obtained via the parallel implementation of the dynamics of stochastic spin systems.