@article{ECP3314,
author = {Louigi Addario-Berry},
title = {Growing random 3-connected maps or Comment s'enfuir de l'Hexagone},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {19},
year = {2014},
keywords = {Random maps, random trees, random planar graphs, growth procedures},
abstract = {We use a growth procedure for binary trees due to Luczak and Winkler, a bijection between binary trees and irreducible quadrangulations of the hexagon due to Fusy, Poulalhon and Schaeffer, and the classical angular mapping between quadrangulations and maps, to define a growth procedure for maps. The growth procedure is local, in that every map is obtained from its predecessor by an operation that only modifies vertices lying on a common face with some fixed vertex. As n tends to infinity, the probability that the n'th map in the sequence is 3-connected tends to 2^8/3^6. The sequence of maps has an almost sure limit G, and we show that G is the distributional local limit of large, uniformly random 3-connected graphs.},
pages = {no. 54, 1-12},
issn = {1083-589X},
doi = {10.1214/ECP.v19-3314},
url = {http://ecp.ejpecp.org/article/view/3314}}