Jakob Björnberg (17/11/14)

Benedikt Magnússon, nóvember 13, 2014

Málstofa í stærðfræði

Fyrirlesari: Jakob Björnberg, Chalmers Tekniska Högskola, Göteborg
Titill: Percolation in random quadrangulations of the half-plane

Staðsetning: V-157, VRII
Tími: Mánudagur 17. nóvember, frá 15:00 til 16:00.

Ágrip:

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.