Itô’s excursion theory and random trees |
| |
Authors: | Jean-Franç ois Le Gall |
| |
Affiliation: | Département de mathématiques, Université Paris-Sud, 91405 Orsay Cédex, France |
| |
Abstract: | We explain how Itô’s excursion theory can be used to understand the asymptotic behavior of large random trees. We provide precise statements showing that the rescaled contour of a large Galton–Watson tree is asymptotically distributed according to Itô’s excursion measure. As an application, we provide a simple derivation of Aldous’ theorem stating that the rescaled contour function of a Galton–Watson tree conditioned to have a fixed large progeny converges to a normalized Brownian excursion. We also establish a similar result for a Galton–Watson tree conditioned to have a fixed large height. |
| |
Keywords: | 60J65 60J80 60C05 |
本文献已被 ScienceDirect 等数据库收录! |