10 papers
Competitive displacement in the grass-bushes-trees process on a scale-free network
John Fernley, Daniel Valesin
The grass-bushes-trees process is a two-type contact process in which the types face asymmetric birth mechanisms. Vertices of a graph can either be occupied by a tree, occupied by…
Percolation of the contact process on the regular tree
John Fernley, Emmanuel Jacob
The contact process on the regular tree when has the two phase transitions of global and of local survival, found by Pemantle and Liggett at values a…
The voter model on the hyperbolic graph
John Fernley, Christian Hirsch
We consider the voter model on the giant component of a hyperbolic random graph, which is a spatial scale-free network, in the sparse and linear-giant regime . We find…
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 co…
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…
Simultaneous Cutoff on the Multitype Configuration Model
John Fernley, Balázs Gerencsér
We find Gaussian cutoff profiles for the total variation distance to stationarity of a random walk on a multiplex network: a finite number of directed configuration models sharing…
The Contact Process on a Graph Adapting to the Infection
John Fernley, Peter Mörters, Marcel Ortgiese
We show existence of a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to the infection t…
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…