• 1 University of Pennsylvania

We study tilings with lozenges of a domain with free boundary conditions on one side. These correspondto boxed symmetric plane partitions. We show that the positions of the horizontal lozenges near the left flatboundary, in the limit, have the same joint distribution as the eigenvalues from a Gaussian Unitary Ensemble (theGUE-corners/minors process). We also prove the existence of a limit shape of the height function (the symmetricplane partition). We also consider domains where the sides converge to $\infty$ at different rates and recover again theGUE-corners process.