New bounds on the density of lattice coverings

2020/05/30 by Ordentlich, Or, Regev, Oded, Weiss, Barak · 4 citations
#11H31 #11T30 #94B75 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.00340

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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