44 citations · 327 across the 39 of their papers we have counts for
12 papers · 1 filter
Random triangulations of the d-sphere with minimum volume
Agelos Georgakopoulos, John Haslegrave, Joel Larsson Danielsson
We study a higher-dimensional analogue of the {Random Travelling Salesman Problem}: let the complete -dimensional simplicial complex on vertices be equipped with i…
Competing types in preferential attachment graphs with community structure
John Haslegrave, Jonathan Jordan, Mark Yarrow
We extend the two-type preferential attachment model of Antunović, Mossel and Rácz, where each new vertex takes its type according to a defined rule based on the types of its neigh…
Combinatorial universality in three-speed ballistic annihilation
John Haslegrave, Laurent Tournier
We consider a one-dimensional system of particles, moving at constant velocities chosen independently according to a symmetric distribution on , and annihilating upon…
A time-invariant random graph with splitting events
Agelos Georgakopoulos, John Haslegrave
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming ed…
Site percolation and isoperimetric inequalities for plane graphs
John Haslegrave, Christoforos Panagiotis
We use isoperimetric inequalities combined with a new technique to prove upper bounds for the site percolation threshold of plane graphs with given minimum degree conditions. In th…
Three-speed ballistic annihilation: phase transition and universality
John Haslegrave, Vladas Sidoravicius, Laurent Tournier
We consider ballistic annihilation, a model for chemical reactions first introduced in the 1980's physics literature. In this particle system, initial locations are given by a rene…
The ballistic annihilation threshold is positive
John Haslegrave
In the ballistic annihilation process, particles on the real line have independent speeds symmetrically distributed in and are annihilated by collisions. It is widely…
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…
Percolation on an infinitely generated group
Agelos Georgakopoulos, John Haslegrave
We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with , in which clusters are almost surely finite for all values of the…
Reaching consensus on a connected graph
John Haslegrave, Mate Puljiz
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the…
Preferential attachment with choice
John Haslegrave, Jonathan Jordan
We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky a…