@article{EJP563,
author = {Marie Albenque and Jean-Francois Marckert},
title = {Some families of increasing planar maps},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {stackmaps, triangulations, Gromov-Hausdorff convergence, continuum random tree},
abstract = {Stack-triangulations appear as natural objects when one wants to define some families of increasing triangulations by successive additions of faces. We investigate the asymptotic behavior of rooted stack-triangulations with $2n$ faces under two different distributions. We show that the uniform distribution on this set of maps converges, for a topology of local convergence, to a distribution on the set of infinite maps. In the other hand, we show that rescaled by $n^{1/2}$, they converge for the Gromov-Hausdorff topology on metric spaces to the continuum random tree introduced by Aldous. Under a distribution induced by a natural random construction, the distance between random points rescaled by $(6/11)\log n$ converge to 1 in probability. We obtain similar asymptotic results for a family of increasing quadrangulations.},
pages = {no. 56, 1624-1671},
issn = {1083-6489},
doi = {10.1214/EJP.v13-563},
url = {http://ejp.ejpecp.org/article/view/563}}