  Ultralight candidates for dark matter can present wavelike features on
astrophysical scales. Full wave based simulations of such candidates are
currently limited to box sizes of 1--10 Mpc/$h$ on a side, limiting our
understanding of the impact of wave dynamics on the scale of the cosmic web. We
present a statistical analysis of density fields produced by perturbative
forward models in boxes of 128 Mpc/$h$ side length. Our wave-based perturbation
theory maintains interference on all scales, and is compared to fluid dynamics
of Lagrangian perturbation theory. The impact of suppressed power in the
initial conditions and interference effects caused by wave dynamics can then be
disentangled. We find that changing the initial conditions captures most of the
change in one-point statistics such as the skewness of the density field.
However, different environments of the cosmic web, quantified by critical
points of the smoothed density, appear to be more sensitive to interference
effects sourced by the quantum potential. This suggests that certain
large-scale summary statistics may need additional care when studying
cosmologies with wavelike dark matter.
