  We perform the first one-point fluctuation analysis of the high-energy
neutrino sky. This method reveals itself to be especially suited to
contemporary neutrino data, as it allows to study the properties of the
astrophysical components of the high-energy flux detected by the IceCube
telescope, even with low statistics and in the absence of point source
detection. Besides the veto-passing atmospheric foregrounds, we adopt a simple
model of the high-energy neutrino background by assuming two main
extra-galactic components: star-forming galaxies and blazars. By leveraging
multi-wavelength data from Herschel and Fermi, we predict the spectral and
anisotropic probability distributions for their expected neutrino counts in
IceCube. We find that star-forming galaxies are likely to remain a diffuse
background due to the poor angular resolution of IceCube, and we determine an
upper limit on the number of shower events that can reasonably be associated to
blazars. We also find that upper limits on the contribution of blazars to the
measured flux are unfavourably affected by the skewness of the blazar flux
distribution. One-point event clustering and likelihood analyses of the IceCube
HESE data suggest that this method has the potential to dramatically improve
over more conventional model-based analyses, especially for the next generation
of neutrino telescopes.
