June 1, 2012
Location: Janskerkhof 15a (Utrecht), room 101
Random walks in a supercritical contact process
Random walks in dynamic random environments are models for diffusion in a randomly evolving medium, which is usually assumed to be Markovian. Many results about the asymptotic behavior of the random walk are available when the medium has sufficiently fast and uniform mixing in space-time, but much less is understood when mixing is non-uniform. I will discuss an example of the latter situation, given by the supercritical contact process.
Spin glasses are spin models in a random environment. Invented by physicists in the 1970s they have raised some the most challenging problems in both, probability and statistical physics, over the past two decades. Only about five years ago, Talagrand was able to rigorously confirm the physicists prediction in one of the most prominent models of a spin glass. Moreover, spin glasses serve as good models in a variety of situations such as neural networks and mathematical economics. In this talk we will motivate some of the basic models and present results on the fluctuations of central observables.