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.

Final version

References in corpus (4)

• Dynamical systems arising from random substitutions
• Random Substitution Tilings and Deviation Phenomena
• Algebras of random operators associated to Delone dynamical systems
• Traces of random operators associated with self-affine Delone sets and Shubin's formula

Cited by in corpus (1)

• Statistical properties of Lorentz gases on aperiodic tilings, Part 1