We study preferential attachment models where vertices enter the network with iid random
numbers of edges that we call the out-degree. We identify the local limit of such models …

Continuous-time branching processes describe the evolution of a population whose
individuals generate a random number of children according to a birth process. Such …

We study a general model of random dynamical simplicial complexes and derive a formula
for the asymptotic degree distribution. This asymptotic formula generalises results for a …

A growing family of random graphs is called robust if it retains a giant component after
percolation with arbitrary positive retention probability. We study robustness for graphs, in …

We study a class of branching processes in which a population consists of immortal
individuals equipped with a fitness value. Individuals produce offspring with a rate given by …

We study a general model of recursive trees where vertices are equipped with independent
weights and at each time-step a vertex is sampled with probability proportional to its fitness …

We introduce the random exponential recursive tree in which at each point of discrete time
every node recruits a child (new leaf) with probability p, or fails to do so with probability 1− p …

We study a generalisation of the random recursive tree (RRT) model and its multigraph
counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a …

Preferential attachment models with fitness are a substantial extension of the classical
preferential attachment model, where vertices have an independent fitness that has a linear …

Preferential attachment models form a popular class of growing networks, where incoming
vertices are preferably connected to vertices with high degree. We consider a variant of this …