Geometry of two-dimensional quantum gravity coupled to O(n) loop models


Many aspects of the fractal geometry of pure two-dimensional quantum gravity are well-understood, thanks to a variety of methods in the enumeration of planar maps and continuum processes in Liouville Quantum Gravity. The presence of coupled matter systems limits the applicability of these methods, and several open questions remain. In this talk I will discuss the generalization of one of these methods, the peeling exploration, to random planar maps coupled to an O(n) loop model. Relying on exact scale-invariance in the scaling limit some explicit distance statistics can be obtained.

Nagoya University, Japan