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PreprintarXiv licencearXiv

The stealthiest particle configurations in 8 and 24 dimensions

  • Alex Cohen
  • Henry Cohn
  • Maryna Viazovska
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Abstract

We show that the E8 and Leech lattices generate the stealthiest isometry-invariant, locally square-integrable point processes of intensity $1$ in ℝ8 and ℝ24, respectively, and that they are the unique stealthiest processes. We also apply the proof technique to sphere packing and energy minimization, and we construct a $20$-dimensional periodic configuration that is stealthier than any known $20$-dimensional lattice with the same particle density. This periodic configuration is a formal dual of Vardy's $20$-dimensional sphere packing.

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Cite

BibTeXRIS
BibTeX
@misc{cohen2026stealthiest,
  title = {{The stealthiest particle configurations in 8 and 24 dimensions}},
  author = {Alex Cohen and Henry Cohn and Maryna Viazovska},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03121},
  eprint = {2609.03121},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03121},
}
RIS
TY  - UNPB
TI  - The stealthiest particle configurations in 8 and 24 dimensions
AU  - Alex Cohen
AU  - Henry Cohn
AU  - Maryna Viazovska
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03121
UR  - https://arxiv.org/abs/2609.03121
AB  - We show that the E_8 and Leech lattices generate the stealthiest isometry-invariant, locally square-integrable point processes of intensity $1$ in ℝ^8 and ℝ^24, respectively, and that they are the unique stealthiest processes. We also apply the proof technique to sphere packing and energy minimization, and we construct a $20$-dimensional periodic configuration that is stealthier than any known $20$-dimensional lattice with the same particle density. This periodic configuration is a formal dual of Vardy's $20$-dimensional sphere packing.
ER  -