Mathematics – Probability
Scientific paper
2005-11-21
Probability Surveys 2005, Vol. 2, 245-311
Mathematics
Probability
Published at http://dx.doi.org/10.1214/154957805100000140 in the Probability Surveys (http://www.i-journals.org/ps/) by the In
Scientific paper
10.1214/154957805100000140
We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple approach to Aldous' theorem giving the convergence in distribution of the contour process of conditioned Galton-Watson trees towards the normalized Brownian excursion. We also briefly discuss applications to combinatorial trees. In the continuous setting, we use the formalism of real trees, which yields an elegant formulation of the convergence of rescaled discrete trees towards continuous objects. We explain the coding of real trees by functions, which is a continuous version of the well-known coding of discrete trees by Dyck paths. We pay special attention to random real trees coded by Brownian excursions, and in a particular we provide a simple derivation of the marginal distributions of the CRT. The last section is an introduction to the theory of the Brownian snake, which combines the genealogical structure of random real trees with independent spatial motions. We introduce exit measures for the Brownian snake and we present some applications to a class of semilinear partial differential equations.
No associations
LandOfFree
Random trees and applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Random trees and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random trees and applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-291231