Typical Voronoi cells for Cox point processes on Manhattan grids

Hinsen, Alexander; Hirsch, Christian; Jahnel, Benedikt; Cali, Élie

doi:10.23919/wiopt47501.2019.9144122

Cited by 1 publication

(2 citation statements)

References 12 publications

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“…Now, we consider the chase-escape model as an independent space-time process on realizations of the connectivity graph. This also brings us much closer to the existing literature on chase-escape dynamics on fixed and random graphs; see, for example, [4,7,15,[21][22][23]39], as chase-escape has not been studied on a dynamic graph so far. More precisely, we consider g ρ,r (S, X λ ∪ Y λ W ) under the Palm distribution with respect to the X λ described in (1) and let N(X i ) denote the set of direct neighbors of vertex X i .…”

Section: Chase-escape On the Connectivity Graphmentioning

confidence: 77%

“…This gives rise to chase-escape processes [4,7,15,21,39] in which malware is transmitted from infected to susceptible devices and infected devices are patched. Again, the main results are concerned with exhibiting regimes of survival and extinction of the malware in the system, and such regimes have also been established in the continuum [22,23].…”

Section: Introduction and Settingmentioning

confidence: 99%

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Chase–escape in dynamic device-to-device networks

Cali,

Hinsen,

Jahnel

et al. 2023

J. Appl. Probab.

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We feature results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in Cali et al. (2022), we consider an urban environment, represented by line segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for a sufficiently long time the infection can be transmitted and then propagates into the system according to the same rule starting from a typical device. Inspired by wireless network architectures, the network is additionally equipped with a second class of agents able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to chase–escape dynamics. We give conditions for parameter configurations that guarantee existence and absence of global survival as well as an in-and-out of the survival regime, depending on the speed of the devices. We also provide complementary results for the setting in which the chase–escape dynamics is defined as an independent process on the connectivity graph. The proofs mainly rest on percolation arguments via discretization and multiscale analysis.

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