Interfacial energies on Penrose lattices

In this paper we prove a homogenization theorem for interfacial discrete energies defined on an a-periodic Penrose tiling in 2. A general result on the homogenization of surface energies cannot be directly adapted to this case; the existence of the limit interfacial energy is therefore proved by showing some refined "quasi-periodic" properties of the tilings. © 2011 World Scientific Publishing Company.