Random skew plane partitions and the Pearcey process

We study random skew 3D partitions weighted by q(vol) and, specifically, the q --> 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.