Continuum percolation for Cox point processes |
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| Institution: | 1. School of Mathematical Sciences, Kean University, Union, NJ, 07083, USA;2. Department of Biostatistics, Mailman School of Public Health, Columbia University, 722 West 168th Street, New York, NY 10032, USA;1. Sorbonne Université, Campus Pierre et Marie Curie Case courrier 158, 4, place Jussieu, 75252 Paris Cedex 05, France;2. University of Birmingham, School of Mathematics, B15 2TT, Birmingham, UK |
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| Abstract: | 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. |
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| Keywords: | Cox processes Percolation Stabilization Large deviations |
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