83 citations · 246 across the 21 of their papers we have counts for
22 papers
Convergence to equilibrium for density dependent Markov jump processes
Andrew Barbour, Graham Brightwell, Malwina Luczak
We investigate the convergence to (quasi--)equilibrium of a density dependent Markov chain in~, whose drift satisfies a system of ordinary differential equations hav…
Long-term concentration of measure and cut-off
Andrew Barbour, Graham Brightwell, Malwina Luczak
We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited…
The mathematics of causal sets
Graham Brightwell, Malwina Luczak
The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interestin…
The greedy independent set in a random graph with given degrees
Graham Brightwell, Svante Janson, Malwina Luczak
We analyse the size of an independent set in a random graph on vertices with specified vertex degrees, constructed via a simple greedy algorithm: order the vertices arbitrarily…
Extinction times in the subcritical stochastic SIS logistic epidemic
Graham Brightwell, Thomas House, Malwina Luczak
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identi…
A fixed-point approximation for a routing model in equilibrium
Graham Brightwell, Malwina Luczak
We use a method of Luczak (arXiv:1212.3231) to investigate the equilibrium distribution of a dynamic routing model on a network. In this model, there are nodes, each pair joine…