The structure of Galton-Watson trees conditioned to be of a given size is wellunderstood. We provide yet another embedding theorem that permits us to obtain asymptotic probabilities of events that are determined by what happens near the root of these trees. As an example, we derive the probability that a Galton-Watson tree is cut when each node is independently removed with probability p, where...

SHUTLER, D., and MULLIE, A. 1991. Size-related foraging behaviour of the leaf-cutting ant Atta colombica. Can. J . Zool. 69: 15301533 In a Costa Rican forest adjacent to cattle pasture, larger individuals of the leaf-cutting ant Atta colombica carried heavier loads and foraged farther from the colony, as predicted by foraging theory. Counter to foraging theory, individual ants did not increase ...

Cutting random recursive trees, and the Bolthausen–Sznitman coalescent Christina Goldschmidt, University of Warwick (joint work with James Martin) The Bolthausen–Sznitman coalescent was introduced in the context of spin glasses in [1]. These days, it is usually thought of as a special case of a more general class of coalescent processes introduced by Pitman [5] and Sagitov [7] and usually refer...

In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSI-design and report on our computational experience. This includes a brief discussion of separation algorithms, a new LP-based primal heuristic and implementation details. The paper is based on the polyhedral theory for the Steiner tree pa...

We study random cutting down of a rooted tree and show that the number of cuts is equal (in distribution) to the number of records in the tree when edges (or vertices) are assigned random labels. Limit theorems are given for this number, in particular when the tree is a random conditioned Galton–Watson tree. We consider both the distribution when both the tree and the cutting (or labels) are ra...

Here we consider two parameters for random non-crossing trees: i the number of random cuts to destroy a sizen non-crossing tree and ii the spanning subtree-size of p randomly chosen nodes in a size-n non-crossing tree. For both quantities, we are able to characterise for n ∞ the limiting distributions. Non-crossing trees are almost conditioned Galton-Watson trees, and it has been already shown,...