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Annales de l’Institut Henri Poincaré D


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Volume 4, Issue 3, 2017, pp. 273–307
DOI: 10.4171/AIHPD/41

Published online: 2017-09-26

Conformal invariance of dimer heights on isoradial double graphs

Zhongyang Li[1]

(1) University of Connecticut, Storrs, USA

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.

Keywords: Dimer model, perfect matching, conformal invariance, Gaussian free field, isoradial graph

Li Zhongyang: Conformal invariance of dimer heights on isoradial double graphs. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 4 (2017), 273-307. doi: 10.4171/AIHPD/41