2005/12/16 by B. de Tilière, B. deTilière
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Combinatorics #Dimension (graph theory) #Dimer #Function (biology) #Gaussian #Gaussian free field #Geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Rhombus #Scaling #Scaling limit #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #math-ph #math.MP #math.PR #msc:60G15 #msc:82B20
paper · pdf · doi:10.1016/j.anihpb.2006.10.002
published as Annales de l'institut Henri Poincaré (B) Probabilités et Statistiques, 43 no. 6 (2007), p. 729-750 · 32 pages, 4 figures
arxiv created 2005/12/16 · openalex publication_date 2007/02/02 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider dimer models on graphs which are bipartite, periodic and satisfy a geometric condition called \em isoradiality, defined in \citeKenyon3. We show that the scaling limit of the height function of any such dimer model is 1/√π times a Gaussian free field. Triangular quadri-tilings were introduced in \citeBea; they are dimer models on a family of isoradial graphs arising form rhombus tilings. By means of two height functions, they can be interpreted as random interfaces in dimension 2+2. We show that the scaling limit of each of the two height functions is 1/√π times a Gaussian free field, and that the two Gaussian free fields are independent.