Related papers: Asymptotics of random domino tilings of rectangula…
This paper establishes a universality result for scaling limits of uniformly random lozenge tilings of large domains. We prove that whenever a boundary of the domain has three adjacent straight segments inclined under 120 degrees to each…
We study asymptotic limit of random pure dimer coverings on rail yardgraphs when the mesh sizes of the graphs go to 0. Each pure dimer covering correspondsto a sequence of interlacing partitions starting with an empty partition and ending…
We compute the algebraic equation for arctic curves of the Aztec diamond with a doubly (quasi-)periodic weight structure and obtain similar results for certain models of the hexagon. In particular, we determine the algebraic degree of such…
We study a family of periodically weighted Aztec diamond dimer models near their turning points. We establish that, asymptotically, as $N\rightarrow\infty$, their fluctuations there, scaled by $\sqrt{N}$, are described by a marked…
In this article we define a generalization of the domino shuffling algorithm for tilings of the Aztec diamond to the interacting $k$-tilings recently introduced by S. Corteel, A. Gitlin, and the first author. We describe the algorithm both…
We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can…
We compute the probability of any local pattern at an arbitrary position in a random dimer configuration in a square grid with an Aztec-diamond boundary.
We use the periodic Schur process, introduced in arXiv:math/0601019v1, to study the random height function of lozenge tilings (equivalently, dimers) on an infinite cylinder distributed under two variants of the $q^{\operatorname{vol}}$…
We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implications on the sophistication degree of an appropriate…
We show that the number of configurations of the 20 Vertex model on certain domains with domain wall type boundary conditions is equal to the number of domino tilings of Aztec-like triangles, proving a conjecture from [P. Di Francesco and…
We review the connections between the octahedral recurrence, $\lambda$-determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the $\lambda$-determinant (and generalizations thereof) of an…
This paper deals with two GUE-matrices, coupled together through some inequalities between the spectra of the first few (small) principal minors. The main results of the paper is to show that the spectra of the principal minors of these…
Let U be a multiply-connected region in R^2 with smooth boundary. Let P_epsilon be a polyomino in epsilon Z^2 approximating U as epsilon tends to 0. We show that, for certain boundary conditions on P_epsilon, the height distribution on a…
In this paper we investigate the height field of a dimer model/random domino tiling on the plane at a smooth-rough (i.e. gas-liquid) transition. We prove that the height field at this transition has two-point correlation functions which…
We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaussian process with independent coefficients when expanded in…
We consider the problem of counting and classifying domino tilings of a quadriculated torus. The counting problem for rectangles was studied by Kasteleyn and we use many of his ideas. Domino tilings of planar regions can be represented by…
We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
We study the limiting behavior of random lozenge tilings of the hexagon with a q-Racah weight as the size of the hexagon grows large. Based on the asymptotic behavior of the recurrence coefficients of the q-Racah polynomials, we give a new…
Rail-yard graphs are a general class of graphs introduced in \cite{bbccr} on which the random dimer coverings form Schur processes. We study asymptotic limits of random dimer coverings on rail yard graphs with free boundary conditions on…