Generalized Tilings with Height
نویسندگان
چکیده
منابع مشابه
An n-Dimensional Generalization of the Rhombus Tiling
Several classic tilings, including rhombuses and dominoes, possess height functions which allow us to 1) prove ergodicity and polynomial mixing times for Markov chains based on local moves, 2) use coupling from the past to sample perfectly random tilings, 3) map the statistics of random tilings at large scales to physical models of random surfaces, and and 4) are related to the “arctic circle” ...
متن کاملA note on the structure of spaces of domino tilings
We study spaces of tilings, formed by tilings which are on a geodesic between two fixed tilings of the same domain (the distance is defined using local flips). We prove that each space of tilings is homeomorphic to an interval of tilings of a domain when flips are classically directed by height functions. © 2006 Elsevier B.V. All rights reserved.
متن کاملGraphs of Tilings
For a given finite set of tiles and a strip of fixed height we describe how to obtain the associated (finite directed) graph that encodes the structure of the set of all possible tilings. We then consider possible constraints on such graphs and introduce and give some preliminary results on the reverse question: Given a graph, does there exist a set of tiles and a fixed height such that the cor...
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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 g...
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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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