Extension of the Brownian-disc method to non-separable planar maps

Determine whether the non-bijective method of Bettinelli, Curien, Fredes, and Sepúlveda for obtaining Brownian-disc scaling limits of quadrangulations with a simple boundary extends to the setting of non-separable planar maps, including the development of suitable restrictions of non-separable planar maps.

Background

The paper compares its common-core transfer method with the method of Bettinelli, Curien, Fredes, and Sepúlveda for quadrangulations with a simple boundary. That method relies on suitable restrictions of a randomly sized core, whereas the present setting concerns non-separable planar maps and lacks an immediately available analogous restriction framework.

The authors identify the transfer of the method to non-separable planar maps as unresolved and note that genuinely new input concerning suitable restrictions would be required. This is a concrete methodological question because a positive answer would extend scaling-limit transfer techniques to planar maps with boundaries and non-separable constraints.