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2020 The contact process with dynamic edges on $\mathbb {Z}$
Amitai Linker, Daniel Remenik
Electron. J. Probab. 25: 1-21 (2020). DOI: 10.1214/20-EJP480


We study the contact process running in the one-dimensional lattice undergoing dynamical percolation, where edges open at rate $vp$ and close at rate $v(1-p)$. Our goal is to explore how the speed of the environment, $v$, affects the behavior of the process. Among our main results we find that: 1. For small enough $v$ the process dies out, while for large $v$ the process behaves like a contact process on $\mathbb {Z}$ with rate $\lambda p$, where $\lambda $ is the birth rate of each particle, so in particular it survives if $\lambda $ is large. 2. For fixed $v$ and small enough $p$ the network becomes immune, in the sense that the process dies out for any infection rate $\lambda $, while if $p$ is sufficiently close to $1$ then for all $v>0$ survival is possible for large enough $\lambda $. 3. Even though the first two points suggest that larger values of $v$ favor survival, this is not necessarily the case for small $v$: when the number of initially infected sites is large enough, the infection survives for a larger expected time in a static environment than in the case of $v$ positive but small. Some of these results hold also in the setting of general (infinite) vertex-transitive regular graphs.


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Amitai Linker. Daniel Remenik. "The contact process with dynamic edges on $\mathbb {Z}$." Electron. J. Probab. 25 1 - 21, 2020.


Received: 21 August 2019; Accepted: 8 June 2020; Published: 2020
First available in Project Euclid: 11 July 2020

zbMATH: 07252712
MathSciNet: MR4125785
Digital Object Identifier: 10.1214/20-EJP480

Primary: 60K35, 60K37


Vol.25 • 2020
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