Tilings and traces
Abstract
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 $\mathbb{R}^d$ 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 Schrödinger operators obtained from aperiodic tilings in the construction.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2021
 DOI:
 10.1063/5.0015534
 arXiv:
 arXiv:1906.00466
 Bibcode:
 2021JMP....62g2701T
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Operator Algebras;
 37H15;
 37B50;
 52C22;
 52C23;
 19K14
 EPrint:
 Final version