The local limit of unicellular maps in high genus
arXiv:1309.6254
Abstract
We show that the local limit of unicellular maps whose genus is proportional to the number of edges is a supercritical geometric Galton-Watson tree conditioned to survive. The proof relies on enumeration results obtained via the recent bijection given by the second author together with Feray and Fusy.
12 pages, 1 figure