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SUMMARY:Mobile geometric graphs: detection\, coverage and percolation - Pe
 rla Sousi ( Statistical Laboratory\, University of Cambridge.)
DTSTART:20110207T143000Z
DTEND:20110207T153000Z
UID:TALK29248@talks.cam.ac.uk
CONTACT:Elena Yudovina
DESCRIPTION:We consider the following dynamic Boolean model introduced by 
 van den Berg\, Meester and White (1997). At time 0\, let the nodes of the 
 graph be a Poisson point process in R^d with constant intensity and let ea
 ch node move independently according to Brownian motion. At any time t\, w
 e put an edge between every pair of nodes if their distance is at most r. 
 We study two features in this model: detection (the time until a target po
 int--fixed or moving--is within distance r from some node of the graph)\, 
 coverage (the time until all points inside a finite box are detected by th
 e graph) and percolation (the time until a given node belongs to the infin
 ite connected component of the graph). We obtain asymptotics for these fea
 tures by combining ideas from stochastic geometry\, coupling and multi-sca
 le analysis. This is joint work with Yuval Peres\, Alistair Sinclair and A
 lexandre Stauffer. 
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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