Tranport estimates for random measures in dimension one

2015/10/13 by Martin Huesmann, Huesmann, Martin · 1 citation
Mathematics · #49Q20 #60G55 #60G57 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1510.03601

openalex publication_date 2015/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there is a sharp threshold in dimension one for the transport cost between the Lebesgue measure λ and an invariant random measure μ of unit intensity to be finite. We show that for any such random measure the L¹ cost are infinite provided that the first central moments 𝔼[|n-μ([0,n))|] diverge. Furthermore, we establish simple and sharp criteria, based on the variance of μ([0,n)], for the L^p cost to be finite for 0

Citations

• The geometry of optimal transportation

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