Abstract: It is already a classical result that the largest components (for example connected components or 2-connected components) in random planar maps have linear expected size and the limiting distribution follows an Airy law. This was systematically studied by Banderier, Flajolet, Schaeffer, and Soria (2001) in the context of critical singularity schemes of generating functions.The main purpose of the present work is to extend these techniques to more general situations, in particular to cores and maximal components of random cubic maps, where several additional technical difficulties appear, in the combinatorial as well in the analytic part.
This is joint work with Marc Noy, Clement Requile, and Juanjo Rue.