Geometry of random surfaces coupled to an O(n) loop model


Understanding the geometry (and in particular the fractal dimensions) of random surfaces when they are coupled to critical matter is one of the main open challenges in two-dimensional quantum gravity. I’ll discuss a small step in this direction in the case of coupling to an O(n) loop model. Using the peeling exploration and machinery from stochastic processes, some explicit distance statistics can be derived.

HG 03.085 (Hilbert Room), Nijmegen, The Netherlands