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 Steinâ€™sâ€¦ (More)

Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number r, the rneighbour bootstrap process isâ€¦ (More)

We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galtonâ€“Watson tree with critical, finite-variance offspring distribution, conditioned to haveâ€¦ (More)

We consider sums of functions of fringe subtrees of binary search trees and random recursive trees (of total size n). The use of Steinâ€™s method and certain couplings allow provision of simple proofsâ€¦ (More)

We consider the model of random trees introduced by Devroye [SIAM J Comput 28, 409â€“ 432, 1998]. The model encompasses many important randomized algorithms and data structures. The pieces of dataâ€¦ (More)

We study the number of records in a random binary search tree on n randomly labelled vertices. Equivalently the number of random cuttings required to eliminate a random binary search tree can beâ€¦ (More)

We study protected nodes inm-ary search trees, by putting them in context of generalised PÃ³lya urns. We show that the number of two-protected nodes (the nodes that are neither leaves nor parents ofâ€¦ (More)

This survey studies asymptotics of random fringe trees and extended fringe trees in random trees that can be constructed as family trees of a Crumpâ€“Modeâ€“Jagers branching process, stopped at aâ€¦ (More)

Majority bootstrap percolation on a graph G is an epidemic process defined in the following manner. Firstly, an initially infected set of vertices is selected. Then step by step the vertices thatâ€¦ (More)

Equip each point x of a homogeneous Poisson point process P onR withDx edge stubs, where theDx are i.i.d. positive integer-valued random variables with distribution given by Î¼. Following the stableâ€¦ (More)