THE SHAPE OF STRETCHED PLANAR TREES

We study the asymptotics of a ''stretched'' model of unlabeled rooted planar trees, in which trees are not taken equiprobable but are weight ed exponentially, according to their height. By using standard methods for computing the probabilities of large deviations of random process es, we show that, as the number of vertices tends to infinity, the nor malized shape of a random tree converges in distribution to a determin istic limit. We compute this limit explicitly. (C) 1995 John Wiley and Sons, Inc.