9 Lectures on dimers Richard Kenyon

Dimers, tilings and trees

Generalizing results of Temperley [11], Brooks, Smith, Stone and Tutte [1] and others [10, 7] we describe a natural equivalence between three planar objects: weighted bipartite planar graphs; planar Markov chains; and tilings with convex polygons. This equivalence provides a measure-preserving bijection between dimer coverings of a weighted bipartite planar graph and spanning trees of the corre...

DFT Application to the Analysis of Quadrupole Coupling Constant of Aluminum Methyl Chloride Dimers

The analysis of the 27Al and 35Cl quadrupole coupling parameters of aluminum methyl chloride dimers were carried out on the basis of the density functional theory (DFT). The available experimental values of quarupole coupling constants were compared with their calculated ones. In this investigation, the correlations were made between calculated 27Al and 35Cl nuclear quadrupole coupling constant...

DFT study of dimers of dimethyl sulfoxide in gas phase

Density functional (DFT) calculations at M05-2x/aug-cc-pVDZ level were used to analyze the interactions between dimethyl sulfoxide (DMSO) dimers. The structures obtained have been analyzed with the Atoms in Molecules (AIMs) and Natural Bond Orbital (NBO) methodologies. Four minima were located on the potential energy surface of the dimers. Three types of interactions are observed, CH•••O, CH•••...

Height fluctuations in the honeycomb dimer model Richard Kenyon

We study a model of random crystalline surfaces arising in the dimer model on the honeycomb lattice. For a fixed “wire frame” boundary condition, as the lattice spacing ǫ → 0, Cohn, Kenyon and Propp [3] showed the almost sure convergence of a random surface to a non-random limit shape Σ0. We show here that when Σ0 has no facets, for a large family of boundary conditions approximating the wire f...

The Planar Dimer Model with Boundary: a Survey