  We study random skew 3D partitions weighted by $q^{\textup{vol}}$ and,
specifically, the $q\to 1$ asymptotics of local correlations near various
points of the limit shape. We obtain sine-kernel asymptotics for correlations
in the bulk of the disordered region, Airy kernel asymptotics near a general
point of the frozen boundary, and a Pearcey kernel asymptotics near a cusp of
the frozen boundary.
