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arXiv · 2606.05105

Stochastically evolving ellipsoids with symmetries

Elisha B. Abuya·Nihar Gargava·Yufei Zhao
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Abstract

We prove that there is a universal constant $c > 0$ such that, along an infinite sequence of dimensions $N$, there are lattice sphere packings in $\mathbb{R}^N$ of density at least $c N^2 \log\log N \, 2^{-N}$, improving the previous best bound due to Klartag by a $\log\log N$ factor. The proof follows Klartag's stochastic ellipsoid evolution process, subject to the cyclotomic symmetries introduced by Venkatesh.

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Elisha B. Abuya, Nihar Gargava, Yufei Zhao. 2026-06-03. Stochastically evolving ellipsoids with symmetries. https://arxiv.org/abs/2606.05105

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