  We consider random lozenge tilings on the triangular lattice with holes
$Q_1,...,Q_n$ in some fixed position. For each unit triangle not in a hole,
consider the average orientation of the lozenge covering it. We show that the
scaling limit of this discrete field is the electrostatic field obtained when
regarding each hole $Q_i$ as an electrical charge of magnitude equal to the
difference between the number of unit triangles of the two different
orientations inside $Q_i$. This is then restated in terms of random surfaces,
yielding the result that the average over surfaces with prescribed height at
the union of the boundaries of the holes is, in the scaling limit, a sum of
helicoids.
