Linear repetitivity beyond abelian groups
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918051212951552 |
|---|---|
| author | Beckus, Siegfried Hartnick, Tobias Pogorzelski, Felix |
| author_facet | Beckus, Siegfried Hartnick, Tobias Pogorzelski, Felix |
| contents | We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weighted Delone sets in homogeneous Lie groups constructed in the companion paper arXiv:2109.15210 using symbolic substitution methods. More generally, using the quasi-tiling method of Ornstein-Weiss, we establish unique ergodicity of hulls of weighted Delone sets in amenable unimodular lcsc groups under a new repetitivity condition which we call tempered repetitivity. For this purpose, we establish a general sub-additive convergence theorem, which also has applications concerning the existence of Banach densities and uniform approximation of the spectral distribution function of finite hopping range operators on Cayley graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_10725 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Linear repetitivity beyond abelian groups Beckus, Siegfried Hartnick, Tobias Pogorzelski, Felix Dynamical Systems We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weighted Delone sets in homogeneous Lie groups constructed in the companion paper arXiv:2109.15210 using symbolic substitution methods. More generally, using the quasi-tiling method of Ornstein-Weiss, we establish unique ergodicity of hulls of weighted Delone sets in amenable unimodular lcsc groups under a new repetitivity condition which we call tempered repetitivity. For this purpose, we establish a general sub-additive convergence theorem, which also has applications concerning the existence of Banach densities and uniform approximation of the spectral distribution function of finite hopping range operators on Cayley graphs. |
| title | Linear repetitivity beyond abelian groups |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2001.10725 |