The â€˜classicalâ€™ random graph models, in particular G(n, p), are â€˜homogeneousâ€™, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in theâ€¦ (More)

A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, forâ€¦ (More)

We use and extend a method by Hoeffding to obtain strong large deviation bounds for sums of dependent random variables with suitable dependency structure. The method is based on breaking up the sumâ€¦ (More)

The asymptotic distribution of the number of Hamilton cycles in a random regular graph is determined. The limit distribution is of an unusual type; it is the distribution of a variable whoseâ€¦ (More)

We study a generalized PÃ³lya urn with balls of two colours and a triangular replacement matrix; the urn is not required to be balanced. We prove limit theorems describing the asymptotic distributionâ€¦ (More)

This is an appendix to [3], and we use the notation there. In particular, if T is a rooted tree, X(T ) denotes the random number of (edge) cuttings needed to destroy the tree completely, orâ€¦ (More)

Consider the minimal weights of paths between two points in a complete graph K n with random weights on the edges, the weights being e.g. uniformly distributed. It is shown that, asymptotically, thisâ€¦ (More)

We study the largest component of a random (multi)graph on n vertices with a given degree sequence. We let nâ†’âˆž. Then, under some regularity conditions on the degree sequences, we give conditions onâ€¦ (More)