Random substitutions are a natural generalisation of their classical 'deterministic'counterpart
, whereby at every step of iterating the substitution, instead of replacing a letter with a …

We study the topology and dynamics of subshifts and tiling spaces associated to non-
primitive substitutions in one dimension. We identify a property of a substitution, which we …

Suppose a set of prototiles allows $ N $ different substitution rules. In this paper we study
tilings of $\mathbb {R}^ d $ constructed from random application of the substitution rules …

In the study of aperiodic order and mathematical models of quasicrystals, questions
regarding equivalence relations on Delone sets naturally arise. This work is dedicated to the …

Pattern-equivariant (PE) cohomology is a well-established tool with which to interpret the
Čech cohomology groups of a tiling space in a highly geometric way. We consider homology …

The study of aperiodic tilings of the plane has a rich history which emerged from the worlds
of computer science and mathematical logic when Berger proved the undecidability of the …

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 …

The mathematical theory of aperiodic order grew out of various predecessors in discrete
geometry, harmonic analysis and mathematical physics, and developed rapidly after the …