  Event-by-event fluctuations are central to the current understanding of
ultrarelativistic heavy-ion collisions. In particular, fluctuations in the
geometry of the early-time collision system are responsible for new phenomena
such as triangular flow, which have solved important puzzles in existing data.
We propose a simple model where initial fluctuations stem from independent flux
tubes randomly distributed in the transverse plane. We calculate analytically
the moments of the initial anisotropies (dipole asymmetry, eccentricity,
triangularity), which are the sources of anisotropic flow, and their mutual
correlations. Our analytic results are in good agreement with calculations from
commonly-used Monte-Carlo codes, providing a simple understanding of the
fluctuations contained in these models. Any deviation from these results in
future experimental data would thus indicate the presence of non-trivial
correlations between the initial flux tubes and/or extra sources of
fluctuations that are not present in current models.
