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CATEGORIES:Optimization and Incentives Seminar
SUMMARY:Mobile geometric graphs: detection\, coverage and
percolation - Perla Sousi ( Statistical Laboratory
\, University of Cambridge.)
DTSTART;TZID=Europe/London:20110207T143000
DTEND;TZID=Europe/London:20110207T153000
UID:TALK29248AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29248
DESCRIPTION:We consider the following dynamic Boolean model in
troduced by van den Berg\, Meester and White (1997
). At time 0\, let the nodes of the graph be a Poi
sson point process in R^d with constant intensity
and let each node move independently according to
Brownian motion. At any time t\, we put an edge be
tween every pair of nodes if their distance is at
most r. We study two features in this model: detec
tion (the time until a target point--fixed or movi
ng--is within distance r from some node of the gra
ph)\, coverage (the time until all points inside a
finite box are detected by the graph) and percola
tion (the time until a given node belongs to the i
nfinite connected component of the graph). We obta
in asymptotics for these features by combining ide
as from stochastic geometry\, coupling and multi-s
cale analysis. This is joint work with Yuval Peres
\, Alistair Sinclair and Alexandre Stauffer.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:Elena Yudovina
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