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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