Some families of increasing planar maps
| dc.creator | Albenque, Marie | |
| dc.creator | Marckert, Jean-François | |
| dc.date | 2007-12-04 | |
| dc.date.accessioned | 2026-07-07T08:47:17Z | |
| dc.date.available | 2026-07-07T08:47:17Z | |
| dc.description | Stack-triangulations appear as natural objects when one wants to define some increasing families of 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. | |
| dc.identifier | https://arxiv.org/abs/0712.0593 | |
| dc.identifier | http://arxiv.org/abs/0712.0593 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143542 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.title | Some families of increasing planar maps | |
| dc.type | text |