5 papers
The contact process on a bipartite spatial network
John Fernley, Christian Hirsch, Daniel Valesin
We study the contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infec…
The Supermarket Model on a Dynamic Regular Hypergraph
John Fernley, Balázs Gerencsér
The supermarket model is a system of queues each with serving rates and arrival rates per vertex, where tasks will move on arrival to the shortest adjacent queue. We c…
The Second Phase Transition of the Contact Process on a Random Regular Graph
John Fernley
The regular tree corresponds to the random regular graph as its local limit. For this reason the famous double phase transition of the contact process on regular tree has been seen…
The Phase Transition of the Voter Model on Evolving Scale-Free Networks
John Fernley
The voter model is a classical interacting particle system explaining consensus formation on a social network. Real social networks feature not only a heterogeneous degree distribu…
Targeted Immunisation Thresholds for the Contact Process on Power-Law Trees
John Fernley, Emmanuel Jacob
Scale-free configuration models are intimately connected to power law Galton-Watson trees. It is known that contact process epidemics can propagate on these trees and therefore the…