  We explore the deep ultraviolet (that is, short-distance) limit of the power
spectrum (PS) and of the correlation function of a cold dark matter dominated
Universe. While for large scales the PS can be written as a double series
expansion, in powers of the linear PS and of the wavenumber $k$, we show that,
in the opposite limit, it can be expressed via an expansion in powers of the
form $1/k^{d+2n}$, where $d$ is the number of spatial dimensions, and $n$ is a
non negative integer. The coefficients of the terms of the expansion are
nonperturbative in the linear PS, and can be interpreted in terms of the
probability density function for the displacement field, evaluated around
specific configurations of the latter, that we identify. In the case of the
Zel'dovich dynamics, these coefficients can be determined analytically, whereas
for the exact dynamics they can be treated as fit, or nuisance, parameters. We
confirm our findings with numerical simulations and discuss the necessary steps
to match our results to those obtained for larger scales and to actual
measurements.
