Speaker
Sigurdur Örn Stefansson
(University of Iceland)
Description
Random planar quadrangulations (and, more generally, random
planar maps) belong to an active field of research in
theoretical physics, probability and combinatorics. In
recent years there has been an enormous progress on
understanding probabilistic aspects of large random planar
maps themselves. The next big step is to add matter to them,
that is, to study models from statistical physics on large
random planar maps. In this talk we consider one such model,
more specifically site percolation on uniform
quadrangulations of the half-plane. In a recent work with
Jakob Björnberg we obtained a sharp estimate on the critical
percolation probability. Building on the work of O. Angel,
we use the so called peeling process to
explore the map and the percolation cluster simultaneously.
I will explain the general method, how it allows us to get
the bounds for quadrangulations and why it is not the
correct approach to the problem.
