Abstract We explore the tree limits recently defined by Elek and Tardos. In particular, we find for many classes of random trees. give general theorems three conditional Galton–Watson trees simply generated trees, split generalized (as here), a continuous-time branching process. These results include, example, labelled ordered recursive preferential attachment binary search

Increasing trees have been introduced by Bergeron, Flajolet and Salvy [1]. This kind of notion covers several well knows classes of random trees like binary search trees, recursive trees, and plane oriented (or heap ordered) trees. We consider the height of increasing trees and prove for several classes of trees (including the above mentioned ones) that the height satisfies EHn ∼ γ logn (for so...

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...

We identify the mean growth of independence number random binary search trees and recursive show normal fluctuations around their means. Similarly we also limit laws for domination variations it these two cases tree models. Our results are an application a recent general theorem Holmgren Janson on fringe in

Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structu...

We prove general limit theorems for sums of functions of subtrees of (random) binary search trees and random recursive trees. The proofs use a new version of a representation by Devroye, and Stein’s method for both normal and Poisson approximation together with certain couplings. As a consequence, we give simple new proofs of the fact that the number of fringe trees of size k = kn in the binary...

Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structu...

This survey studies asymptotics of random fringe trees and extended fringe trees in random trees that can be constructed as family trees of a Crump–Mode–Jagers branching process, stopped at a suitable time. This includes random recursive trees, preferential attachment trees, fragmentation trees, binary search trees and (more generally) m-ary search trees, as well as some other classes of random...

Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method a general transfer theorem is derived, which allows to establish a limit law on the basis of the recursive structure ...

We consider a Bernoulli bond percolation on a random recursive tree of size n ≫ 1, with supercritical parameter pn = 1 − c/ lnn for some c > 0 fixed. It is known that with high probability, there exists then a unique giant cluster of size Gn ∼ e−c, and it follows from a recent result of Schweinsberg [22] that Gn has non-gaussian fluctuations. We provide an explanation of this by analyzing the e...