  We define the correlation of holes on the triangular lattice under periodic
boundary conditions and study its asymptotics as the distances between the
holes grow to infinity. We prove that the joint correlation of an arbitrary
collection of lattice-triangular holes of even sides satisfies, for large
separations between the holes, a Coulomb law and a superposition principle that
perfectly parallel the laws of two dimensional electrostatics, with physical
charges corresponding to holes, and their magnitude to the difference between
the number of right-pointing and left-pointing unit triangles in each hole.
  We detail this parallel by indicating that, as a consequence of our result,
the relative probabilities of finding a fixed collection of holes at given
mutual distances (when sampling uniformly at random over all unit rhombus
tilings of the complement of the holes) approaches, for large separations
between the holes, the relative probabilities of finding the corresponding two
dimensional physical system of charges at given mutual distances. Physical
temperature corresponds to a parameter refining the background triangular
lattice.
  We give an equivalent phrasing of our result in terms of covering surfaces of
given holonomy. From this perspective, two dimensional electrostatics arises by
averaging over all possible discrete geometries of the covering surfaces.
