A sequence of trees $(\mathcal {T} _ {n}) _ {n\in\mathbb {N}} $ contains a\emph {persistent
hub}, or displays\emph {degree centrality}, if there is a fixed node of maximal degree for all …

We introduce a model of evolving preferential attachment trees where vertices are assigned
weights, and the evolution of a vertex depends not only on its own weight, but also on the …

We study the evolution of the graph distance and weighted distance between two fixed
vertices in dynamically growing random graph models. More precisely, we consider …

We introduce a model of a preferential attachment based random graph which extends the
family of models in which condensation phenomena can occur. Each vertex has an …

We consider the preferential attachment model with location-based choice introduced by
Haslegrave et al.(Random Struct Algorithms 56 (3): 775–795, 2020) as a model in which …

In this paper we define a family of preferential attachment models for random graphs with
fitness in the following way: independently for each node, at each time step a random fitness …

In this thesis we define a class of competing growth processes, which is a generalisation of
reinforced branching processes [26]. The class encompasses different preferential …

This thesis is concerned with two classes of evolving random graph models in random
environment: preferential attachment models with additive fitness, as originally defined in …

We introduce general models of evolving, inhomogeneous random structures, where in
each of the models either one or several nodes arrive at a time, and are equipped with …

We investigate the use of stochastic approximation as a method of identifying conditions
necessary to facilitate condensation and coexistence. We did this for a variety of preferential …