We study the asymptotics of a “stretched” model of unlabeled rooted planar trees, in which trees are not taken equiprobable but are weighted exponentially, according to their height. By using standard methods for computing the probabilities of large deviations of random processes, we show that, as the number of vertices tends to infinity, the normalized shape of a random tree converges in distribution to a deterministic limit. We compute this limit explicitly. © 1995 John Wiley & Sons, Inc.
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Applied Mathematics