Statistics of gamma-ray point sources below the Fermi detection limit
  An analytic relation between the statistics of photons in pixels and the
number counts of multi-photon point sources is used to constrain the
distribution of gamma-ray point sources below the Fermi detection limit at
energies above 1 GeV and at latitudes below and above 30 degrees. The derived
source-count distribution is consistent with the distribution found by the
Fermi collaboration based on the first Fermi point source catalogue. In
particular, we find that the contribution of resolved and unresolved active
galactic nuclei (AGN) to the total gamma-ray flux is below 20% - 25%. In the
best fit model, the AGN-like point source fraction is 17% +- 2%. Using the fact
that the Galactic emission varies across the sky while the extra-galactic
diffuse emission is isotropic, we put a lower limit of 51% on Galactic diffuse
emission and an upper limit of 32% on the contribution from extra-galactic weak
sources, such as star-forming galaxies. Possible systematic uncertainties are
discussed.
