  Bootstrap percolation has been used effectively to model phenomena as diverse
as emergence of magnetism in materials, spread of infection, diffusion of
software viruses in computer networks, adoption of new technologies, and
emergence of collective action and cultural fads in human societies. It is
defined on an (arbitrary) network of interacting agents whose state is
determined by the state of their neighbors according to a threshold rule. In a
typical setting, bootstrap percolation starts by random and independent
"activation" of nodes with a fixed probability $p$, followed by a deterministic
process for additional activations based on the density of active nodes in each
neighborhood ($\theta$ activated nodes). Here, we study bootstrap percolation
on random geometric graphs in the regime when the latter are (almost surely)
connected. Random geometric graphs provide an appropriate model in settings
where the neighborhood structure of each node is determined by geographical
distance, as in wireless {\it ad hoc} and sensor networks as well as in
contagion. We derive bounds on the critical thresholds $p_c', p_c"$ such that
for all $p > p"_c(\theta)$ full percolation takes place, whereas for $p <
p'_c(\theta)$ it does not. We conclude with simulations that compare numerical
thresholds with those obtained analytically.
