Conformal invariance of dimer heights on isoradial double graphs
نویسنده
چکیده
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.
منابع مشابه
Conformal invariance of isoradial dimer models & the case of triangular quadri-tilings
We consider dimer models on graphs which are bipartite, periodic and satisfy a geometric condition called isoradiality, defined in [18]. We show that the scaling limit of the height function of any such dimer model is 1/ √ π times a Gaussian free field. Triangular quadri-tilings were introduced in [6]; they are dimer models on a family of isoradial graphs arising form rhombus tilings. By means ...
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تاریخ انتشار 2015