2000/04/01 by Richard Kenyon · 2 citations
Mathematics · #Point processes and geometric inequalities #Random Matrices and Applications #Stochastic processes and statistical mechanics #Mathematics #Conformal map #Invariant (physics) #Domino #Conformal symmetry #Boundary (topology) #Combinatorics #Mathematical analysis #Distribution (mathematics) #Mathematical physics
paper · pdf · doi:10.1214/aop/1019160260
openalex publication_date 2000/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26
Let U be a multiply connected region in R^ 2 with smooth boundary. Let Pε be a polyomino in \epsilonZ2 approximating U as ε → 0.We show that, for certain boundary conditions on P_\eqsilon, the height distribution on a random domino tiling (dimer covering) of P_\eqsilon is conformally invariant in the limit as ε tends to 0, in the sense that the distribution of heights of boundary components (or rather, the difference of the heights from their mean values) only depends on the conformal type of U. The mean height is not strictly conformally invariant but transforms analytically under conformal mappings in a simple way. The mean height and all the moments are explicitly evaluated.