Growth procedure for non-separable planar maps

Construct a growth procedure for the target model of non-separable planar maps that generates a random map with a prescribed larger size from one with a smaller size via controlled local modifications, thereby enabling the Tauberian scaling-limit approach used for irreducible quadrangulations.

Background

A recent approach for irreducible quadrangulations transfers scaling limits from unconstrained quadrangulations by means of a growth procedure relating consecutive sizes through local modifications. The paper explains that an analogous tool is not available for non-separable planar maps.

Such a procedure would provide a way to control the geometric effect of the characteristic n^{2/3}-scale fluctuations in core size and could yield an alternative route to the scaling limit established in the paper.