Open Access
Translator Disclaimer
March 2016 A Poisson allocation of optimal tail
Roland Markó, Ádám Timár
Ann. Probab. 44(2): 1285-1307 (March 2016). DOI: 10.1214/15-AOP1001

Abstract

The allocation problem for a $d$-dimensional Poisson point process is to find a way to partition the space to parts of equal size, and to assign the parts to the configuration points in a measurable, “deterministic” (equivariant) way. The goal is to make the diameter $R$ of the part assigned to a configuration point have fast decay. We present an algorithm for $d\geq3$ that achieves an $O(\operatorname{exp}(-cR^{d}))$ tail, which is optimal up to $c$. This improves the best previously known allocation rule, the gravitational allocation, which has an $\operatorname{exp}(-R^{1+o(1)})$ tail. The construction is based on the Ajtai–Komlós–Tusnády algorithm and uses the Gale–Shapley–Hoffman–Holroyd–Peres stable marriage scheme (as applied to allocation problems).

Citation

Download Citation

Roland Markó. Ádám Timár. "A Poisson allocation of optimal tail." Ann. Probab. 44 (2) 1285 - 1307, March 2016. https://doi.org/10.1214/15-AOP1001

Information

Received: 1 March 2013; Revised: 1 December 2014; Published: March 2016
First available in Project Euclid: 14 March 2016

zbMATH: 1338.60027
MathSciNet: MR3474472
Digital Object Identifier: 10.1214/15-AOP1001

Subjects:
Primary: 60D05

Rights: Copyright © 2016 Institute of Mathematical Statistics

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.44 • No. 2 • March 2016
Back to Top