Continuum percolation for Cox point processes
- Hirsch, Christian
- Jahnel, Benedikt
- Cali, Elie
2010 Mathematics Subject Classification
- 60F10 60K35
- Cox processes, percolation, stabilization, large deviations
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.
- Stochastic Process. Appl., 366 (2019), pp. 139--172 (published online on 20.11.2018), DOI 10.1016/j.spa.2018.11.002 .