Conformal invariance of dimer heights on isoradial double graphs

Zhongyang Li

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arXiv · 1309.0151

Conformal invariance of dimer heights on isoradial double graphs

Zhongyang Li

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Abstract

An isoradial graph is a planar graph in which each face is inscribable into a circle of common radius. We study the 2-dimensional perfect matchings on a bipartite isoradial graph, obtained from the union of an isoradial graph and its interior dual graph. Using the isoradial graph to approximate a simply-connected domain bounded by a simple closed curve, by letting the mesh size go to zero, we prove that in the scaling limit, the distribution of height is conformally invariant and converges to a Gaussian free field.

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Zhongyang Li. 2013-08-31. Conformal invariance of dimer heights on isoradial double graphs. https://arxiv.org/abs/1309.0151

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