18 citations · 46 across the 12 of their papers we have counts for
13 papers
Critical branching processes in random environment with immigration and an application to randomised reproducing graphs
Simon Irons, Jonathan Jordan
We study branching processes in an i.i.d.\ random environment with immigration in the critical regime, where the underlying offspring mechanism satisfies the critical condition tha…
Fragility of non-convergence in preferential attachment graphs with three types
Ben Andrews, Jonathan Jordan
Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have ma…
Phase transitions in non-linear urns with interacting types
Marcelo Costa, Jonathan Jordan
We investigate reinforced non-linear urns with interacting types, and show that where there are three interacting types there are phenomena which do not occur with two types. In a…
Extensive Condensation in a model of Preferential Attachment with Fitnesses
Nic Freeman, Jonathan Jordan
We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this…
Condensation in preferential attachment models with location-based choice
John Haslegrave, Jonathan Jordan, Mark Yarrow
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 associated uni…
Non-convergence of proportions of types in a preferential attachment graph with three co-existing types
John Haslegrave, Jonathan Jordan
We consider the preferential attachment model with multiple vertex types introduced by Antunović, Mossel and Rácz. We give an example with three types, based on the game of rock-pa…