Random real trees

Details Random real trees Random real trees

2006-05-17

arxiv.org/abs/math/0605484v1

Annales Fac. Sci. Toulouse Ser. 6, Vol. XV, pp. 35-62, 2006

Mathematics

Probability

25 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Random real trees 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 real trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random real trees will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-489984