Rigorous scaling limits for statistically decorated planar maps

Establish rigorous scaling-limit convergence for statistically decorated random planar maps beyond the bounded-degree pure-gravity regime, including convergence to the corresponding Liouville quantum gravity surfaces and conformal loop ensembles.

Background

The introduction places FK-decorated planar maps within a broader program relating discrete random surfaces to Liouville quantum gravity and conformal loop ensembles. Although substantial convergence results are known for bounded-degree maps, the authors state that rigorous convergence in the general setting of maps coupled to critical statistical-mechanics models remains unresolved. This is a broader open problem than the critical q=4 hamburger-cheeseburger scaling limit proved in the paper.