A Poisson allocation of optimal tail

Details A Poisson allocation of optimal tail A Poisson allocation of optimal tail

2011-03-27

arxiv.org/abs/1103.5259v2

Mathematics

Probability

22 pages, 1 figure

Scientific paper

The allocation problem for a Poisson point process is to find a way to partition the space to parts of equal size, and assign the parts to the configuration points in a measurable, "deterministic" (equivariant) way. The goal is to make the diameter of the part assigned to a configuration point have fast decay. We present an algorithm for $d\geq 3$, that achieves an $O(\exp (-cR^d))$ tail, which is optimal up to $c$. This improves the best previously known allocation rule, the gravitational allocation, which has $\exp (-cR ^{1+o(1)})$ tail.

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