1.1. Description of results. A domino is a 1×2 (or 2×1) rectangle, and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps. In 1961,… (More)

We show how to compute the probability of any given local configuration in a random tiling of the plane with dominos. That is, we explicitly compute the measures of cylinder sets for the measure of… (More)

We give a construction of a self-similar tiling of the plane with any prescribed expansion coefficient λ ∈ C (satisfying the necessary algebraic condition of being a complex Perron number). For any… (More)

We show that the dimer model on a bipartite graph Γ on a torus gives rise to a quantum integrable system of special type, which we call a cluster integrable system. The phase space of the classical… (More)

We define a scaling limit of the height function on the domino tiling model (dimer model) on simplyconnected regions in Z and show that it is the “massless free field”, a Gaussian process with… (More)

Given a finite or infinite planar graph all of whose faces have degree 4, we study embeddings in the plane in which all edges have length 1, that is, in which every face is a rhombus. We give a… (More)

We compute some large-scale properties of the uniform spanning tree process on Z 2. In particular we compute certain crossing probabilities for rectangles and annuli.