Gracar, P orcid.org/0000-0001-8340-8340 and Stauffer, A (2019) Multi-scale Lipschitz percolation of increasing events for Poisson random walks. Annals of Applied Probability, 29 (1). pp. 376-433.
Abstract
Consider the graph induced by Zd , equipped with uniformly elliptic random conductances. At time 0, place a Poisson point process of particles on Zd and let them perform independent simple random walks. Tessellate the graph into cubes indexed by i ∈ Zd and tessellate time into intervals indexed by τ . Given a local event E(i,τ) that depends only on the particles inside the space time region given by the cube i and the time interval τ , we prove the existence of a Lipschitz connected surface of cells (i,τ) that separates the origin from infinity on which E(i,τ) holds. This gives a directly applicable and robust framework for proving results in this setting that need a multi-scale argument. For example, this allows us to prove that an infection spreads with positive speed among the particles.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright © 2019 Institute of Mathematical Statistics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Multi-scale percolation; Lipschitz surface; spread of infection |
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: | 28 Nov 2023 13:22 |
Last Modified: | 28 Nov 2023 17:49 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/18-AAP1420 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200622 |