Poisson allocations with bounded connected cells

2014/10/09 by Alexander E. Holroyd, Holroyd, Alexander E., Jean Martin +1
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1410.2642

openalex publication_date 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a homogenous Poisson point process in the plane, we prove that it is possible to partition the plane into bounded connected cells of equal volume, in a translation-invariant way, with each point of the process contained in exactly one cell. Moreover, the diameter D of the cell containing the origin satisfies the essentially optimal tail bound P(D>r)

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