Scaling limit of isoradial dimer models and the case of triangular quadri-tilings |
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Authors: | Batrice de Tilire |
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Institution: | aInstitut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland |
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Abstract: | We consider dimer models on planar graphs which are bipartite, periodic and satisfy a geometric condition called isoradiality, defined in R. Kenyon, The Laplacian and Dirac operators on critical planar graphs, Invent. Math. 150 (2) (2002) 409–439]. We show that the scaling limit of the height function of any such dimer model is a Gaussian free field. Triangular quadri-tilings were introduced in B. de Tilière, Quadri-tilings of the plane, math.PR/0403324, Probab. Theory Related Fields, in press]; they are dimer models on a family of isoradial graphs arising from rhombus tilings. By means of two height functions, they can be interpreted as random interfaces in dimension 2+2. We show that the scaling limit of each of the two height functions is a Gaussian free field, and that the two Gaussian free fields are independent. |
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Keywords: | Dimer model Gausian free field Scaling limit Height function Quadri-tilings |
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