Two-point cluster function for continuum percolation

We introduce a two-point cluster function C₂(r ₁,r₂) which reflects information about clustering in general continuum-percolation models. Specifically, for any two-phase disordered medium, C₂(r₁,r₂) gives the probability of finding both points r₁ and r₂ in the same cluster of one of the phases. For distributions of identical inclusions whose coordiantes are fully specified by center-of-mass positions (e.g., disks, spheres, oriented squares, cubes, ellipses, or ellipsoids, etc.), we obtain a series representation of C₂ which enables one to compute the two-point cluster function. Some general asymptotic properties of C₂ for such models are discussed. The two-point cluster function is then computed for the adhesive-sphere model of Baxter. The two-point cluster function for arbitrary media provides a better signature of the microstructure than does a commonly employed two-point correlation function defined in the text.