Drewitz, A., Gallo, G. and Gracar, P. orcid.org/0000-0001-8340-8340 (Accepted: 2024) Lipschitz cutset for fractal graphs and applications to the spread of infections. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. ISSN: 0246-0203 (In Press)
Abstract
We consider the fractal Sierpiński gasket or carpet graph in dimension denoted by . At time , we place a Poisson point process of particles onto the graph and let them perform independent simple random walks, which in this setting exhibit sub-diffusive behaviour. We generalise the concept of particle process dependent Lipschitz percolation to the (coarse graining of the) space-time graph , where the opened/closed state of space-time cells is measurable with respect to the particle process inside the cell. We then provide an application of this generalised framework and prove the following: if particles can spread an infection when they share a site of , and if they recover independently at some rate , then if is sufficiently small, the infection started with a single infected particle survives indefinitely with positive probability.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article accepted for publication in Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Sep 2025 12:59 |
Last Modified: | 25 Sep 2025 13:30 |
Status: | In Press |
Publisher: | Institute of Mathematical Statistics |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:231954 |