Conformal invariance of domino tiling

1999/10/01 by Richard Kenyon, Kenyon, Richard · 4 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.math-ph/9910002

openalex publication_date 1999/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U be a multiply-connected region in R² with smooth boundary. Let P_epsilon be a polyomino in epsilon Z² approximating U as epsilon tends to 0. We show that, for certain boundary conditions on P_epsilon, the height distribution on a random domino tiling (dimer covering) of P_epsilon is conformally invariant in the limit as epsilon tends to 0, in the sense that the distribution of heights of boundary components only depends on the conformal type of U. The mean height and all the moments are explicitly evaluated.

Cited by

• Uniform spanning trees and random matrix statistics
• Entropy of full covering of the kagome lattice by straight trimers
• Kenyon's identities for the height function and compactified free field in the dimer model
• A quantum N-dimer model

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