Lower bounds for sphere packing in arbitrary norms
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910915814752256 |
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| author | Schildkraut, Carl |
| author_facet | Schildkraut, Carl |
| contents | We show that in any $d$-dimensional real normed space, unit balls can be packed with density at least \[\frac{(1-o(1))d\log d}{2^{d+1}},\] improving a result of Schmidt from 1958 by a logarithmic factor and generalizing the recent result of Campos, Jenssen, Michelen, and Sahasrabudhe in the $\ell_2$ norm. Our main tools are the graph-theoretic result used in the $\ell_2$ construction and volume bounds from convex geometry due to Petty and Schmuckenschläger. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower bounds for sphere packing in arbitrary norms Schildkraut, Carl Metric Geometry Combinatorics We show that in any $d$-dimensional real normed space, unit balls can be packed with density at least \[\frac{(1-o(1))d\log d}{2^{d+1}},\] improving a result of Schmidt from 1958 by a logarithmic factor and generalizing the recent result of Campos, Jenssen, Michelen, and Sahasrabudhe in the $\ell_2$ norm. Our main tools are the graph-theoretic result used in the $\ell_2$ construction and volume bounds from convex geometry due to Petty and Schmuckenschläger. |
| title | Lower bounds for sphere packing in arbitrary norms |
| topic | Metric Geometry Combinatorics |
| url | https://arxiv.org/abs/2406.07479 |