26 citations · 62 across the 12 of their papers we have counts for
18 papers
On balance properties of hypercubic billiard words
Nicolas Bédaride, Valérie Berthé, Antoine Julien
This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order…
Spectral triples for higher-rank graph -algebras
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this note, we present a new way to associate a spectral triple to the noncommutative -algebra of a strongly connected finite higher-rank graph . We generalize a…
Spectral triples and wavelets for higher-rank graphs
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this paper, we present a new way to associate a finitely summable spectral triple to a higher-rank graph , via the infinite path space of . Moreover, we prove t…
Statistics of patterns in typical cut and project sets
Alan Haynes, Antoine Julien, Henna Koivusalo +1
In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic…
Wavelets and spectral triples for higher-rank graphs
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this paper, we present two new ways to associate a spectral triple to a higher-rank graph . Moreover, we prove that these spectral triples are intimately connected to the wav…
Wavelets and spectral triples for fractal representations of Cuntz algebras
Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2
In this article we provide an identification between the wavelet decompositions of certain fractal representations of algebras of directed graphs of M. Marcolli and A. Paoluc…