This material has been published in
Commun. Math. Phys.
302 (2011), 253-289,
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and Christian Krattenthaler
The interaction of a gap with a free boundary in a
two dimensional dimer system
Let l be a fixed vertical lattice line of the unit triangular
lattice in the plane, and let H be the half
plane to the left of l. We consider lozenge tilings of H
that have a triangular gap of side-length two
and in which l is a free boundary - i.e., tiles are allowed to
protrude out half-way across l. We prove
that the correlation function of this gap near the free boundary has
asymptotics 1/(4\pi r), when r tends to infinity,
where r is the distance from the gap to the free boundary. This
parallels the electrostatic phenomenon by which the
field of an electric charge near a conductor can be obtained by the
method of images.
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