Year: 2026
Type: preprint
Abstract: We show that the $E_8$ and Leech lattices generate the stealthiest isometry-invariant, locally square-integrable point processes of intensity $1$ in $\mathbb{R}^8$ and $\mathbb{R}^{24}$, 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.
Source: arXiv (Cornell University)
Authors: Cohen, Alex, Cohn, Henry, Viazovska, Maryna
Institution: New York University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208750627