| Título: | Some families of increasing planar maps |
| Autores: |
Albenque, Marie; LIAFA, Université Paris 7 Marckert, Jean-Francois; LaBRI, Université Bordeaux |
| Fecha: | 2008-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
stackmaps, triangulations, Gromov-Hausdorff convergence, continuum random tree 60C05, 60F1 |
| Descripción: | 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. |
| Idioma: | No aplica |
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