one of the most visible aspects of a forest stand structure is the spatial patterns of trees. competition affects on forest structure and its understanding is important, when the purpose of forest management is to imitate the dynamic of natural ecosystems. for this purpose, an unmanaged intact forest was selected with 26 hectares area. all chestnut leaf oak (quercus castaneifolia) trees with a ...

We study the quantity distance between node j and node n in a random tree of size n chosen from a family of increasing trees. For those subclass of increasing tree families, which can be constructed via a tree evolution process, we give closed formulæ for the probability distribution, the expectation and the variance. Furthermore we derive a distributional decomposition of the random variable c...

Simply generated families of trees are described by the equation T (z) = φ(T (z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ {1, . . . , n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are ...

Bénédicte Haas, University of Paris-Dauphine, France Limits of Non-increasing Markov Chains and Applications to Random Trees and Coalescents Consider a non-increasing Markov chain with values in the set of non-negative integers, starting from a large integer !. We describe its scaling limit as ! → ∞, under the assumption that the large jump events are rare and happen at rates that behave like a...

This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...