Highly irregular separated nets

Dymond M, Kaluza V. Highly irregular separated nets. arXiv, 1903.05923.

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Author
Dymond, Michael; Kaluza, VojtechIST Austria
Department
Abstract
In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such notions also give rise to distinct equivalence classes. Put differently, we find occurrences of particularly strong divergence of separated nets from the integer lattice. Our approach generalises that of Burago and Kleiner and McMullen which takes place largely in a continuous setting. Existence of irregular separated nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞). In the present work we obtain stronger types of non-realisable densities.
Publishing Year
Date Published
2021-07-14
Journal Title
arXiv
Acknowledgement
This work was supported by Austrian Science Fund (FWF): P 30902-N35.
Article Number
1903.05923
Page
52
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Cite this

Dymond M, Kaluza V. Highly irregular separated nets. arXiv.
Dymond, M., & Kaluza, V. (n.d.). Highly irregular separated nets. arXiv.
Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” ArXiv, n.d.
M. Dymond and V. Kaluza, “Highly irregular separated nets,” arXiv. .
Dymond M, Kaluza V. Highly irregular separated nets. arXiv, 1903.05923.
Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” ArXiv, 1903.05923.
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