TALK BY P. Sousi
Mobile geometric graphs: detection, coverage and percolation
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 each node move
independently according to Brownian motion. At any time t, we 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 point--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 the graph) and
percolation (the time until a given node belongs to the infinite connected
component of the graph). We obtain asymptotics for these features by combining
ideas from stochastic geometry, coupling and multi-scale analysis.
This is joint work with Yuval Peres, Alistair Sinclair and Alexandre Stauffer.