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A functional central limit theorem for SI processes on configuration model graphs

KhudaBukhsh, Wasiur R.; Woroszylo, Casper; Rempa?a, Grzegorz A.; Koeppl, Heinz

Authors

Casper Woroszylo

Grzegorz A. Rempa?a

Heinz Koeppl



Abstract

We study a stochastic compartmental susceptible–infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued càdlàg functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of computer viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.

Citation

KhudaBukhsh, W. R., Woroszylo, C., RempaƂa, G. A., & Koeppl, H. (2022). A functional central limit theorem for SI processes on configuration model graphs. Advances in Applied Probability, 54(3), 880-912. https://doi.org/10.1017/apr.2022.52

Journal Article Type Article
Acceptance Date Sep 25, 2021
Online Publication Date Sep 6, 2022
Publication Date Sep 6, 2022
Deposit Date Sep 9, 2022
Publicly Available Date Mar 7, 2023
Journal Advances in Applied Probability
Print ISSN 0001-8678
Electronic ISSN 1475-6064
Publisher Applied Probability Trust
Peer Reviewed Peer Reviewed
Volume 54
Issue 3
Pages 880-912
DOI https://doi.org/10.1017/apr.2022.52
Keywords Applied Mathematics; Statistics and Probability
Public URL https://nottingham-repository.worktribe.com/output/10919587
Publisher URL https://www.cambridge.org/core/journals/advances-in-applied-probability/article/abs/functional-central-limit-theorem-for-si-processes-on-configuration-model-graphs/8ECE68C7706243E769C7B4BF565C8F3E
Additional Information Copyright: © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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