New lower bound on ball packing density in high-dimensional hyperbolic spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909326849867776 |
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| author | Fernández, Irene Gil Kim, Jaehoon Liu, Hong Pikhurko, Oleg |
| author_facet | Fernández, Irene Gil Kim, Jaehoon Liu, Hong Pikhurko, Oleg |
| contents | We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor Ω(m(R+\ln m)) as m tends to infinity. This is done by applying the recent theorem of Campos, Jenssen, Michelen and Sahasrabudhe on independent sets in graphs with sparse neighbourhoods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07818 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New lower bound on ball packing density in high-dimensional hyperbolic spaces Fernández, Irene Gil Kim, Jaehoon Liu, Hong Pikhurko, Oleg Combinatorics Metric Geometry We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor Ω(m(R+\ln m)) as m tends to infinity. This is done by applying the recent theorem of Campos, Jenssen, Michelen and Sahasrabudhe on independent sets in graphs with sparse neighbourhoods. |
| title | New lower bound on ball packing density in high-dimensional hyperbolic spaces |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2405.07818 |