New bounds on the density of lattice coverings

Or Ordentlich; Oded Regev; Barak Weiss

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arXiv · 2006.00340

New bounds on the density of lattice coverings

Or Ordentlich·Oded Regev·Barak Weiss

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Abstract

We obtain new upper bounds on the minimal density of lattice coverings of Euclidean space by dilates of a convex body K. We also obtain bounds on the probability (with respect to the natural Haar-Siegel measure on the space of lattices) that a randomly chosen lattice L satisfies that L+K is all of space. As a step in the proof, we utilize and strengthen results on the discrete Kakeya problem.

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Or Ordentlich, Oded Regev, Barak Weiss. 2020-05-30. New bounds on the density of lattice coverings. https://arxiv.org/abs/2006.00340

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