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2020 Phase transitions for chase-escape models on Poisson–Gilbert graphs
Alexander Hinsen, Benedikt Jahnel, Elie Cali, Jean-Philippe Wary
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP306


We present results on phase transitions of local and global survival in a two-species model on Poisson–Gilbert graphs. Initially, there is an infection at the origin that propagates on the graph according to a continuous-time nearest-neighbor interacting particle system. The graph consists of susceptible nodes and nodes of a second type, which we call white knights. The infection can spread on susceptible nodes without restriction. If the infection reaches a white knight, this white knight starts to spread on the set of infected nodes according to the same mechanism, with a potentially different rate, giving rise to a competition of chase and escape. We show well-definedness of the model, isolate regimes of global survival and extinction of the infection and present estimates on local survival. The proofs rest on comparisons to the process on trees, percolation arguments and finite-degree approximations of the underlying random graphs.


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Alexander Hinsen. Benedikt Jahnel. Elie Cali. Jean-Philippe Wary. "Phase transitions for chase-escape models on Poisson–Gilbert graphs." Electron. Commun. Probab. 25 1 - 14, 2020.


Received: 5 December 2019; Accepted: 8 March 2020; Published: 2020
First available in Project Euclid: 26 March 2020

zbMATH: 1434.60194
MathSciNet: MR4089732
Digital Object Identifier: 10.1214/20-ECP306

Primary: 60J25 , 60K35 , 60K37

Keywords: Boolean model , extinction , interacting particle systems , percolation , Random graphs , survival


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