## Jakob Björnberg (17/11/14)

Math Colloquium

### Speaker: Jakob Björnberg, Chalmers Tekniska Högskola, Göteborg

Title: Percolation in random quadrangulations of the half-plane

Location: V-157, VRII

Time: Monday, November 17 at 15:00-16:00.

### Abstract:

The topic of random planar quadrangulations (and, more generally, random planar maps) is of interest to probabilists, combinatorialists and physicists alike. Recent years have seen considerable progress on understanding large random planar maps themselves, and the next big challenge is to understand maps “with matter”; that is, to study models from statistical physics on large random planar maps. In this talk we consider such a model, specifically site percolation on uniform quadrangulations of the half-plane. The talk is based on ongoing work together with Sigurdur Stefansson (Reykjavik) where we use a “spatial Markovian property” of the quadrangulations (first described by O. Angel) to study the percolation phase transition. We will describe this Markovian property, see how Angel (et al) used it in the case of triangulations, and discuss results and challenges for the case of quadrangulations.