63 citations · 293 across the 35 of their papers we have counts for
37 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…
Cutoff for the logistic SIS epidemic model with self-infection
Roxanne He, Malwina Luczak, Nathan Ross
We study a variant of the classical Markovian logistic SIS epidemic model on a complete graph, which has the additional feature that healthy individuals can become infected without…
A note on the Markovian SIR epidemic on a random graph with given degrees
Malwina Luczak
This paper provides an additional probabilistic interpretation of the limiting functions for the SIR epidemic on the configuration model derived in the paper by Janson, Luczak and…
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…
Extinction time for the weaker of two competing SIS epidemics
Fabio Lopes, Malwina Luczak
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in th…
Multivariate approximation in total variation, II: discrete normal approximation
A. D. Barbour, Malwina J. Luczak, Aihua Xia
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in . We illustrate the use of the method f…