Random real trees
| dc.creator | Gall, J. F. Le | |
| dc.date | 2006-05-17 | |
| dc.date.accessioned | 2026-07-07T07:14:21Z | |
| dc.date.available | 2026-07-07T07:14:21Z | |
| dc.description | We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning stable trees, including their branching property, which is analogous to the well-known property of Galton-Watson trees, and the calculation of their fractal dimension. We then consider spatial trees, which combine the genealogical structure of a real tree with spatial displacements, and we explain their connections with superprocesses. In the last section, we deal with a particular conditioning problem for spatial trees, which is closely related to asymptotics for random planar quadrangulations. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605484 | |
| dc.identifier | http://arxiv.org/abs/math/0605484 | |
| dc.identifier | Annales Fac. Sci. Toulouse Ser. 6, Vol. XV, pp. 35-62, 2006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112841 | |
| dc.subject | Probability | |
| dc.subject | 60J80;05C80 | |
| dc.title | Random real trees | |
| dc.type | text |