Publication: Quadri-tilings of the plane
Quadri-tilings of the plane
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de Tilière, B. (2007). Quadri-tilings of the plane. Probability Theory and Related Fields, 137(3–4), 487–518. https://doi.org/10.1007/s00440-006-0002-9
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We introduce quadri-tilings and show that they are in bijection with dimer models on a family of graphs R * arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called triangular quadri-tilings, as an interface model in dimension 2+2. Assigning “critical" weights to edges of R *, we prove an explicit expression, only depending on the local geometry of the graph R *, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of Kenyon (Invent Math 150
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- de Tilière, B
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de Tilière, B. (2007). Quadri-tilings of the plane. Probability Theory and Related Fields, 137(3–4), 487–518. https://doi.org/10.1007/s00440-006-0002-9
