  After reviewing some basic relevant properties of stationary stochastic
processes (SSP), we discuss the properties of the so-called Harrison-Zeldovich
like spectra of mass density perturbations. These correlations are a
fundamental feature of all current standard cosmological models. Examining them
in real space we note they imply a "sub-poissonian" normalised variance in
spheres $\sigma_M^2(R) \sim R^{-4} \ln R$. In particular this latter behaviour
is at the limit of the most rapid decay ($\sim R^{-4}$) of this quantity
possible for any stochastic distribution (continuous or discrete). In a simple
classification of all SSP into three categories, we highlight with the name
``super-homogeneous'' the properties of the class to which models like this,
with $P(0)=0$, belong. In statistical physics language they are well described
as lattice or glass-like. We illustrate their properties through two simple
examples: (i) the ``shuffled'' lattice and the One Component Plasma at thermal
equilibrium.
