  In this article we derive the average and the variance of the
cross-correlation of a noise wavefield. The noise cross-correlation function
(NCF) is widely used to passively estimate the Green's function between two
probes and is proportional to the cross density of states (CDOS) in photonic
and plasmonic systems. We first explain from the ladder approximation how the
diffusion halo plays the role of secondary sources to reconstruct the mean
Green's function. We then show that fluctuations of NCF are governed by several
non-Gaussian correlations. An infinite-range NCF correlation dominates CDOS
fluctuations and proves that NCF is not a self averaging quantity with respect
to the plurality of noise sources. The link between these correlations and the
intensity ones is highlighted. These results are supported by numerical
simulations and are of importance for passive imaging applications and material
science.
