The SINR percolation model with random powers is shown to have both a subcritical and a supercritical phase under weaker conditions on the power distribution than previously known.
Continuum percolation for Cox point processes
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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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math.PR 1years
2019 1verdicts
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Percolation phase transitions for the SIR model with random powers
The SINR percolation model with random powers is shown to have both a subcritical and a supercritical phase under weaker conditions on the power distribution than previously known.