Given a random distribution of impurities on a periodic crystal, an equivalent uniquely ergodic tiling space is built, made of aperiodic, repetitive tilings with finite local complexity, and with configurational entropy close to the entropy of the impurity distribution. The construction is the tiling analog of the Jewett-Kreger theorem. In memory of Pierre… (More)
Strictly ergodic spaces of tilings with positive entropy are constructed using tools from information and probability theory. Statistical estimates are made to create a one-dimensional subshift with these dynamical properties, yielding a space of repetitive tilings of R D with finite local complexity that is also equivalent to a symbolic dynamical system… (More)
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and the characterization of the support of such limiting distributions. Such results are known for particles with positions on a fixed lattice; we extend these results to systems of particles on R n , with restrictions on the interaction.