Tilings and traces

This paper deals with (globally) random substitutions on a finite set of prototiles. Using renormalization tools applied to objects from operator algebras, we establish upper and lower bounds on the rate of deviations of ergodic averages for the uniquely ergodic Rd action on the tiling spaces obtained from such tilings. We apply the results to obtain statements about the convergence rates for integrated density of states for random Schrodinger operators obtained from aperiodic tilings in the construction.

Automated summary

This paper focuses on globally random substitutions on a finite set of prototiles, using renormalization tools applied to objects from operator algebras to establish upper and lower bounds on the rate of deviations of ergodic averages for the uniquely ergodic Rd action on the tiling spaces obtained from such tilings. These results are applied to statements about the convergence rates for integrated density of states for random Schrodinger operators obtained from aperiodic tilings in the construction.