  We prove that the electronic density of states (DOS) for 2D incommensurate
layered structures, where Bloch theory does not apply, is well-defined as the
thermodynamic limit of finite clusters. In addition, we obtain an explicit
representation formula for the DOS as an integral over local configurations.
Next, based on this representation formula, we propose a novel algorithm for
computing electronic structure properties in incommensurate heterostructures,
which overcomes limitations of the common approach to artificially strain a
large supercell and then apply Bloch theory.
