Flux calculations in an inhomogeneous Universe: weighting a flux-limited
  galaxy sample
  Many astrophysical problems arising within the context of ultra-high energy
cosmic rays, very-high energy gamma rays or neutrinos, require calculation of
the flux produced by sources tracing the distribution of galaxies in the
Universe. We discuss a simple weighting scheme, an application of the method
introduced by Lynden-Bell in 1971, that allows the calculation of the flux sky
map directly from a flux-limited galaxy catalog without cutting a
volume-limited subsample. Using this scheme, the galaxy distribution can be
modeled up to large scales while representing the distribution in the nearby
Universe with maximum accuracy. We consider fluctuations in the flux map
arising from the finiteness of the galaxy sample. We show how these
fluctuations are reduced by the weighting scheme and discuss how the remaining
fluctuations limit the applicability of the method.
