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Dominos and the Gaussian free field

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arxiv math-ph/0002027 v1 pith:OI3IJL5J submitted 2000-02-09 math-ph math.MP

R. Kenyon This is my paper · ORCID
classification math-phmath.MP
keywords fieldfreegaussianmodelcoefficientsdefinedimerdomino
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We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian.

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  1. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

    math.PR 2025-07 conditional novelty 7.0 of 10

    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

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