  We investigate and quantify the impact of mixed (cold and warm) dark matter
models on large-scale structure observables. In this scenario, dark matter
comes in two phases, a cold one (CDM) and a warm one (WDM): the presence of the
latter causes a suppression in the matter power spectrum which is allowed by
current constraints and may be detected in present-day and upcoming surveys. We
run a large set of $N$-body simulations in order to build an efficient and
accurate emulator to predict the aforementioned suppression with percent
precision over a wide range of values for the WDM mass, $M_\mathrm{wdm}$, and
its fraction with respect to the totality of dark matter, $f_\mathrm{wdm}$. The
suppression in the matter power spectrum is found to be independent of changes
in the cosmological parameters at the 2% level for $k\lesssim 10 \ h/$Mpc and
$z\leq 3.5$. In the same ranges, by applying a baryonification procedure on
both $\Lambda$CDM and CWDM simulations to account for the effect of feedback,
we find a similar level of agreement between the two scenarios. We examine the
impact that such suppression has on weak lensing and angular galaxy clustering
power spectra. Finally, we discuss the impact of mixed dark matter on the shape
of the halo mass function and which analytical prescription yields the best
agreement with simulations. We provide the reader with an application to galaxy
cluster number counts.
