5 papers
A parallel wakeup problem and multi-room light switch strategies
John Haslegrave, Paul A. Russell, Mark Walters
The wakeup problem in distributed computing asks for a symmetric protocol that enables one of several processors to eventually guarantee that all (or, in a more general setting, en…
Balanced two-type annihilation: mean-field asymptotics
John Haslegrave, Peter Keevash
We consider an interacting particle system where equal-sized populations of two types of particles move by random walk steps on a graph, the two types may have different speeds, an…
Sharp thresholds for NAC-colourings and stable cuts in random graphs
Katie Clinch, John Haslegrave, Tony Huynh +1
NAC-colourings of graphs correspond to flexible quasi-injective realisations in . A special class of NAC-colourings are those that arise from stable cuts. We give s…
Dissipative particle systems on expanders
John Haslegrave, Peter Keevash
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different s…
Lonely passengers: a short proof
John Haslegrave
A fixed number of passengers independently board one of several buses uniformly at random. The lonely passenger problem is to prove that the probability of at least one passenger b…