Malwina Luczak

Long-term concentration of measure and cut-off

AD Barbour, G Brightwell, M Luczak

Journal article  |  2022  |  Stochastic Processes and their Applications

We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wa..

EXTINCTION TIME FOR THE WEAKER OF TWO COMPETING SIS EPIDEMICS

Fabio Lopes, Malwina Luczak

Journal article  |  2020  |  ANNALS OF APPLIED PROBABILITY

We consider a simple Markov model for the spread of a disease caused by two virus strains in a closed homogeneously mixing populat..

Component structure of the configuration model: Barely supercritical case

Remco van der Hofstad, Svante Janson, Malwina Luczak

Journal article  |  2019  |  RANDOM STRUCTURES & ALGORITHMS

We study near-critical behavior in the configuration model. Let Dn be the degree of a random vertex and (Formula presented.); we c..

The Supermarket Model with Bounded Queue Lengths in Equilibrium

Graham Brightwell, Marianne Fairthorne, Malwina J Luczak

Journal article  |  2018  |  JOURNAL OF STATISTICAL PHYSICS

In the supermarket model, there are n queues, each with a single server. Customers arrive in a Poisson process with arrival rate λ..

Extinction times in the subcritical stochastic SIS logistic epidemic

Malwina Luczak, Graham Brightwell, Thomas House

Journal article  |  2018  |  JOURNAL OF MATHEMATICAL BIOLOGY

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic m..

MULTIVARIATE APPROXIMATION IN TOTAL VARIATION, I: EQUILIBRIUM DISTRIBUTIONS OF MARKOV JUMP PROCESSES

AD Barbour, MJ Luczak, A Xia

Journal article  |  2018  |  ANNALS OF PROBABILITY

For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variat..

MULTIVARIATE APPROXIMATION IN TOTAL VARIATION, II: DISCRETE NORMAL APPROXIMATION

AD Barbour, MJ Luczak, A Xia

Journal article  |  2018  |  ANNALS OF PROBABILITY

The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in Zd ...

The Greedy Independent Set in a Random Graph with Given Degrees

Graham Brightwell, Svante Janson, Malwina Luczak

Journal article  |  2017  |  RANDOM STRUCTURES & ALGORITHMS

We analyse the size of an independent set in a random graph on n vertices with specified vertex degrees, constructed via a simple ..

Near-critical SIR epidemic on a random graph with given degrees

Svante Janson, Malwina Luczak, Peter Windridge, Thomas House

Journal article  |  2017  |  JOURNAL OF MATHEMATICAL BIOLOGY

Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, ..

The mathematics of causal sets

Graham Brightwell, Malwina Luczak

Book Chapter  |  2016