Dominos and the Gaussian Free Field

2001/07/01 by Richard Kenyon · 3 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Random Matrices and Applications #Gaussian free field #Mathematics #Scaling limit #Gaussian #Gaussian process #Laplace operator #Scaling #Field (mathematics) #Limit (mathematics) #Combinatorics #Mathematical analysis #Pure mathematics #Geometry #Quantum mechanics #Physics

paper · pdf · doi:10.1214/aop/1015345599

openalex publication_date 2001/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We define a scaling limit of the height function on the domino tiling model (dimer model) on simply connected regions in Z² and show that it is the “massless free field,” a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian.

Citations

• Conformal invariance of domino tiling
• Scaling limits of loop-erased random walks and uniform spanning trees
• Long-range properties of spanning trees

Cited by

• Scaling limit of isoradial dimer models and the case of triangular quadri-tilings
• Oded Schramm: From circle packing to SLE
• Gaussian free field [wikipedia]