Height Function on Domino Tilings
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چکیده
We first define the height function on a domino tiling (as done in [1]) and state some of its basic properties. We then revisit the coupling function and relate it to Green’s function, which allows us to conclude that the coupling function converges in the limit to an analytic function with a pole. Using this, we do a general second moment calculation via the proof found in [1] which writes the moment in terms of integrals of functions which are conformally invariant.
منابع مشابه
A 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.
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