Autocorrelation Functions <---> Pair Correlation Functions Are there any ways to convert an autocorrelation function to a pair correlation function, and vice versa?
 A: You define the density auto-correlation function as
$$S_{\rho\rho} = \langle \delta \rho(\mathbf{x}_1) \delta \rho(\mathbf{x}_2)\rangle$$
where $\delta \rho(\mathbf{x}) = \rho(\mathbf{x}) - \langle \rho(\mathbf{x}) \rangle$ is deviation from the local mean value. 
The Fourier transform of $S_{\rho\rho}$ is related to the structure-factor
$$S(\mathbf{q}) = \langle \rho \rangle^2 (2\pi)^d \delta(\mathbf{q}) + \frac{1}{V}\int d^d x_1 d^d x_2 e^{-i \mathbf{q} \cdot (\mathbf{x}_1-\mathbf{x}_2)} S_{\rho\rho}$$
where $\langle \rho \rangle$ is the average density of the whole system, i.e., $V \langle \rho \rangle = \int d^d \mathbf{x} \, \rho(\mathbf{x})$.
The structure factor $S(\mathbf{q})$ is related to the pair-correlation function $g(\mathbf{x})$ via
$$S(\mathbf{q}) = \langle \rho \rangle \Big[1 + \langle \rho \rangle \int d^d \mathbf{x} \, g(\mathbf{x}) e^{-i \mathbf{q} \cdot \mathbf{x}} \Big]$$
If the system is isotropic, then $g(\mathbf{x}) = g(|\mathbf{x}|)$ is called the radial-distribution function.
Most of these relations are already in the wikipedia page linked in the question.
