MARK KAC SEMINAR

In this lecture I review some more or less classical results on the convergence of point processes of extremes of random variables. The key observation is that the resulting limits are fairly insensitive to dependence of the random variables considered.

I will discuss applications in the statistical mechanics of spin glasses, in partitioning problems, and to the “peak sidelobe” problem for non-periodic auto-correlation of random sequences.

We consider a two-dimensional lattice gas consisting of two types of particles, subject to Kawasaki dynamics at low temperature, in a large finite box with an open boundary. Inside the box, nearest neighbouring particles of different type have negative interaction. At the boundary of the box particles are created and annihilated in a way that mimics the presence of an infinite gas reservoir, where the two different types have different densities.

Our aim is to study the gas-liquid phase transition. In particular, we identify the region of parameters for which this transition exhibits metastable behavior, compute the transition time and give a characterization of the “critical” configurations.