Probing the gamma-ray source populations with photon count statistics and anisotropies

The global contribution of unresolved gamma-ray point sources to the extragalactic gamma-ray background has been recently measured using analyses employing the statistical properties of observed gamma-ray counts down to gamma-ray fluxes lower than those reached with standard source detection techniques. In addition, a new measurement of the angular power spectrum (APS) of the unresolved gamma-ray background was recently performed, using 8 years of data of the \emph{Fermi}-LAT. However, the contribution from each specific source classes to the source-count distribution, such as blazars, misaligned Active Galactic Nuclei, or Star Forming Galaxies is affected by significant uncertainties, in particular in the unresolved flux regime. This translates into significantly different predictions for the source-count distribution as a function of energy. We here investigate the statistics of photon counts of more than 10 years of \emph{Fermi}-LAT data and the new APS results to probe the extra-galactic gamma-ray source populations in different energy bands.