Multifractal analysis of measures arising from random substitutions
A Mitchell, A Rutar - Communications in Mathematical Physics, 2024 - Springer
We study regularity properties of frequency measures arising from random substitutions,
which are a generalisation of (deterministic) substitutions where the substituted image of …
which are a generalisation of (deterministic) substitutions where the substituted image of …
Topological mixing of random substitutions
We investigate topological mixing of compatible random substitutions. For primitive random
substitutions on two letters whose second eigenvalue is greater than one in modulus, we …
substitutions on two letters whose second eigenvalue is greater than one in modulus, we …
Substitutions and their Generalisations
N Mañibo - Israel Journal of Chemistry, 2024 - Wiley Online Library
Tilings and point sets arising from substitutions are classical mathematical models of
quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding …
quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding …
On word complexity and topological entropy of random substitution subshifts
A Mitchell - Proceedings of the American Mathematical Society, 2024 - ams.org
We consider word complexity and topological entropy for random substitution subshifts. In
contrast to previous work, we do not assume that the underlying random substitution is …
contrast to previous work, we do not assume that the underlying random substitution is …
Mixing properties and entropy bounds of a family of Pisot random substitutions
We consider a two-parameter family of random substitutions and show certain combinatorial
and topological properties they satisfy. We establish that they admit recognisable words at …
and topological properties they satisfy. We establish that they admit recognisable words at …
[HTML][HTML] Automorphism groups of random substitution subshifts
We prove that for a suitably nice class of random substitutions, their corresponding subshifts
have automorphism groups that contain an infinite simple subgroup and a copy of the …
have automorphism groups that contain an infinite simple subgroup and a copy of the …
Topological mixing of random n-bonacci substitutions
JR Mijares, EJ Sinajon, ED Miro - AIP Conference Proceedings, 2024 - pubs.aip.org
We consider shift spaces generated by maps that send a letter from a finite alphabet to a
finite collection of words over the same alphabet called random substitutions. In particular …
finite collection of words over the same alphabet called random substitutions. In particular …
Aperiodic tilings, order, and randomness
R Treviño - Notices of the American Mathematical Society, 2023 - ams.org
In 1619, Kepler published his Harmonices Mundi (Harmonies of the World), a volume of five
books discussing mathematics, physics, astrology, and music. In Book II, Kepler sets out to …
books discussing mathematics, physics, astrology, and music. In Book II, Kepler sets out to …
A classification of intrinsic ergodicity for recognisable random substitution systems
P Gohlke, A Mitchell - arXiv preprint arXiv:2411.06201, 2024 - arxiv.org
We study a class of dynamical systems generated by random substitutions, which contains
both intrinsically ergodic systems and instances with several measures of maximal entropy …
both intrinsically ergodic systems and instances with several measures of maximal entropy …
Rauzy fractals of random substitutions
We develop a theory of Rauzy fractals for random substitutions, which are a generalisation
of deterministic substitutions where the substituted image of a letter is determined by a …
of deterministic substitutions where the substituted image of a letter is determined by a …