  We present an analysis of the two-point spatial correlation functions of
high-mass X-ray binary (HMXB) and young star cluster (YSC) populations in M31
and M33. We find evidence that HMXBs are spatially correlated with YSCs to a
higher degree than would be expected from random chance in both galaxies. When
supplemented with similar studies in the Milky Way, Small Magellanic Cloud, and
NGC 4449, we find that the peak value of the spatial correlation function
correlates strongly with the specific star formation rate of the host galaxy.
We additionally perform an X-ray stacking analysis of 211 non-X-ray detected
YSCs in M31 and 463 YSCs in M33. We do not detect excess X-ray emission at the
stacked cluster locations down to 3$\sigma$ upper limits of $\sim10^{33}$ erg
s$^{-1}$ (0.35-8 keV) in both galaxies, which strongly suggests that dynamical
formation within YSCs is not a major HMXB formation channel. We interpret our
results in the context of (1) the recent star formation histories of the
galaxies, which may produce differences in the demographics of compact objects
powering the HMXBs, and (2) the differences in natal kicks experienced by
compact objects during formation, which can eject newly-formed HMXB from their
birth clusters.
