The probability of finding a second particle as a function of distance from an initial particle; this probability is found from a statistical average over the system concerned (for example a liquid). A trivial case of the pair distribution function, denoted g(x), is an ideal gas consisting of point particles; in this case the function is independent of position, with g(x) = 1. The pair distribution function relates structure, interparticle interactions, and scattering experiments. Simplifications in the calculation of the pair distribution function arise when the system is homogeneous and translationally invariant. The function features strongly in the theory of liquids.