  A statistical mechanics model for a faceted crystal is the 3D Ising model at
zero temperature. It is assumed that in one octant all sites are occupied by
atoms, the remaining ones being empty. Allowed atom configurations are such
that they can be obtained from the filled octant through successive removals of
atoms with breaking of precisely three bonds. If V denotes the number of atoms
removed, then the grand canonical Boltzmann weight is q^V, 0<q<1. As shown by
Cerf and Kenyon, in the limit q -> 1 a deterministic shape is attained, which
has the three facets (100), (010), (001), and a rounded piece interpolating
between them. We analyse the step statistics as q -> 1. In the rounded piece it
is given by a determinantal process based on the discrete sine-kernel. Exactly
at the facet edge, the steps have more space to meander. Their statistics is
again determinantal, but this time based on the Airy-kernel. In particular, the
border step is well approximated by the Airy process, which has been obtained
previously in the context of growth models. Our results are based on the
asymptotic analysis for space-time inhomogeneous transfer matrices.
