• Corpus ID: 119741285

# Universal optimality of the $E_8$ and Leech lattices and interpolation formulas

@article{Cohn2019UniversalOO,
title={Universal optimality of the \$E\_8\$ and Leech lattices and interpolation formulas},
author={Henry Cohn and Abhinav Kumar and Stephen D. Miller and Danylo V. Radchenko and Maryna S. Viazovska},
journal={arXiv: Metric Geometry},
year={2019}
}
• Published 13 February 2019
• Mathematics
• arXiv: Metric Geometry
We prove that the $E_8$ root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions $8$ and $24$, respectively. In other words, they minimize energy for every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians), which is a strong form of robustness not previously known for any configuration in more than one dimension. This theorem implies their recently shown…

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