Linear repetitivity, I. Uniform subadditive ergodic theorems and applications

This paper is concerned with the concept of linear repetitivity in the theo ry of tilings. We prove a general uniform subadditive ergodic theorem for l inearly repetitive tilings. This theorem unifies and extends various known (sub)additive ergodic theorems on tilings. The results of this paper can be applied in the study of both random operators and lattice gas models on ti lings.