Continuum percolation for Cox point processes

TL;DR

This paper studies continuum percolation in Cox point processes, providing conditions for percolation regimes and asymptotic probabilities, revealing universal and sensitive behaviors depending on the regime.

Contribution

It introduces new conditions for percolation regimes and asymptotic expressions for percolation probability in Cox processes, highlighting universality and dependence on the intensity measure.

Findings

Conditions for sub- and super-critical percolation regimes

Asymptotic formulas for percolation probability

Identification of regimes with universal or sensitive behavior

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.