科研之友
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摘要
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, r -> 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.
- 出版日期2011-2
