Random Tilings of High Symmetry: I. Mean-Field Theory

We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configura-tional entropy of free boundary rhombus tilings in two dimensions. We base our mean-field theory on an iterative tiling construction inspired by the work of de Bruijn. In addition to the entropy, we consider correlation functions, pha-son elasticity and the thermodynamic limit. Tilings of dimension other than two are considered briefly. KEY WORDS: Random tiling; mean field theory; quasicrystal; entropy. 1