##### This material has been published in
Commun. Math. Phys.
**302** (2011), 253-289,
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##
Mihai Ciucu
and Christian Krattenthaler

# The interaction of a gap with a free boundary in a
two dimensional dimer system

### (38 pages)

**Abstract.**
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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