  The description of the statistical properties of dust emission gives
important constraints on the physics of the interstellar medium but it is also
a useful way to estimate the contamination of diffuse interstellar emission in
the cases where it is considered a nuisance. The main goals of this analysis of
the power spectrum and non-Gaussian properties of 100 micron dust emission are
1) to estimate the power spectrum of interstellar matter density in three
dimensions, 2) to review and extend previous estimates of the cirrus noise due
to dust emission and 3) to produce simulated dust emission maps that reproduce
the observed statistical properties. The main results are the following. 1) The
cirrus noise level as a function of brightness has been previously
overestimated. It is found to be proportional to <I> instead of <I>^1.5, where
<I> is the local average brightness at 100 micron. This scaling is in
accordance with the fact that the brightness fluctuation level observed at a
given angular scale on the sky is the sum of fluctuations of increasing
amplitude with distance on the line of sight. 2) The spectral index of dust
emission at scales between 5 arcmin and 12.5 degrees is <gamma>=-2.9 on average
but shows significant variations over the sky. Bright regions have
systematically steeper power spectra than diffuse regions. 3) The skewness and
kurtosis of brightness fluctuations is high, indicative of strong
non-Gaussianity. 4) Based on our characterization of the 100 micron power
spectrum we provide a prescription of the cirrus confusion noise as a function
of wavelength and scale. 5) Finally we present a method based on a modification
of Gaussian random fields to produce simulations of dust maps which reproduce
the power spectrum and non-Gaussian properties of interstellar dust emission.
