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Mobile geometric graphs: detection, coverage and percolation
Ist Teil von
Probability theory and related fields, 2013-06, Vol.156 (1-2), p.273-305
Ort / Verlag
Berlin/Heidelberg: Springer-Verlag
Erscheinungsjahr
2013
Quelle
EBSCOhost Business Source Ultimate
Beschreibungen/Notizen
We consider the following dynamic Boolean model introduced by van den Berg et al. (Stoch. Process. Appl. 69:247–257,
1997
). At time 0, let the nodes of the graph be a Poisson point process in
with constant intensity and let each node move independently according to Brownian motion. At any time
t
, we put an edge between every pair of nodes whose distance is at most
r
. We study three fundamental problems in this model: detection (the time until a target point—fixed or moving—is within distance
r
of some node of the graph); coverage (the time until all points inside a finite box are detected by the graph); and percolation (the time until a given node belongs to the infinite connected component of the graph). We obtain precise asymptotics for these quantities by combining ideas from stochastic geometry, coupling and multi-scale analysis.