  We investigate continuum percolation for Cox point processes, that is,
Poisson point processes driven by random intensity measures. First, we derive
sufficient conditions for the existence of non-trivial sub- and super-critical
percolation regimes based on the notion of stabilization. Second, we give
asymptotic expressions for the percolation probability in large-radius,
high-density and coupled regimes. In some regimes, we find universality,
whereas in others, a sensitive dependence on the underlying random intensity
measure survives.
